I've seen many of the "The Bats think the the Pha/Fentons are the four horses of the apocalypse" idea and wanted to put my own spin on it. In my take the bats are completely wrong about it, the Fe/Phantoms are NOT the four horses, but coincidences start lining up, and they really don't like it.
This is a long one because it takes a WHOLE lot of explaining for how mine is different, and how the bats see them as the horses of the apocalypse through sheer coincidence at first, before the Pha/Fentons Commit to the Bit.
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Danny arrives first of course. He tried to be white with black mane and blue eyes, choosing not to have his Alicorn form mimic the colours of his Ghost form, but of his living form, but he is simply too powerful in his ghost form to have that kind of fine control yet. His eyes are green, his fur is a pale white-green and his hair is a dark grey-green, all his choices tainted with the excess power of his ectoplasm. He arrives through the summoning of the cult, Damian asks to Adopt the big Alicorn pony, and Danny rolls with it, deciding that since he hasn't talked yet, he won't talk at all.
When Dani hears of what's happening, of course she wants to join in and meet THE Bats. She transforms herself into an Alicorn, Much smaller than Danny with white fur on black mane with green eyes, as she see's herself as more Ghost than Human (having been made to BE the "half-Ghost" Vlad would raise) but still want's to be clearly recognized as related to Danny (to keep the Bats from trying to kick her out, not knowing they'd literally never do that).
She comes through a portal Danny makes for her straight into the Batcave. She Arrives right as the Bats convene for a debriefing after a patrol night. She's there all of ten seconds before Damian swoops in to introduce himself and acclimate the new Alicorn to him.
Dani quickly attaches herself to Damian as "her" Bat, because he's extremely attentive of her needs and she's realized that that's something she had never truly experienced before. (Can we blame the other Fe/Phantoms though? Danny was busy with protecting Amity and then being Ghost King, Jazz was busy being the attentive parental figure Danny never had as well as trying to study psychology, Dan/te was not around at all, and Vlad is Vlad, not a Pha/Fenton)
Jazz and Dan/te come to the Cave together, Jazz came because she wanted a first hand look at what Vigilante's psych's are like without the conflict of interest of being directly related to the vigilante, and Dan/te followed her because Jazz is his "parole officer" since he's still going through rehabilitation. Unlike in others interpretations of this setup, Jazz doesn't come through as the red horse of war. She comes through as Famine, Black furred and "Red" (Orange) maned. She wanted to keep her hair colour, and since she was the only reason Dan/te was coming, she let him pick the colour of her fur. Dante is the Red horse of war. after choosing Jazz's Fur colour, he decides to simply be an inverted colour scheme to her, thinking that Danny/Dani had also been inverted colours of each other. (he was wrong, woops.)
When Jazz and Dan/te arrive, Jason is the first one to make the connection that they might be the Four horses of the Apocalypse, and the reason they "arrived" out of order is because "Death" was summoned by the cult in place of the "king of the dead", instead of arriving on his own.
Most of the Batfam brush this off because the first one to arrive on their own, Dani, hasn't really portrayed any real "Conquest" or "Pestilence" like attributes since her arrival. Bruce still calls up John Constantine to come by to take a look/offer his expertise because he's the most versed direct contact he has in this realm of knowledge, and he wants to be sure. Bruce is still doubtful at this point, so he doesn't try and rush Constantine.
The day after Jazz and Dan/te arrive, the Batfam get a mild shock at the fact the hay they had first put out for Danny when he was brought home has actually been eaten. Danny and Dani hadn't touched any yet, because they're able to sustain themselves as half-ghosts with the ambient ectoplasm. Dan/te is also perfectly capable of this since he is full Ghost.
Jazz? Jazz is liminal, sure, but she's still fully alive and needs to eat, and being transformed by outside power has taken a bigger toll on her than she thought it would. She's started eating hay simply because she knows that Dan/te had watched MLP before going evil and is really good at using his Ectoplasm to shape things and goes all in on whatever he's doing, so she figures it won't hurt to try. She's right of course, and she does indeed eat things a proper pony would. Seeing the black horse (Famine) being the only one to eat, REALLY makes Jason smug about his idea that they are the Four Horses, and Bruce quickly calls John again to try and hurry him over.
Within a few days, before John can arrive, The Bats see Dani "sweating" Ectoplasm and Danny lending his own Ectoplasm to keep her stable. She's pretty stable these days, but she's still a clone that was (never)born unstable. Holding an Alicorn form is rather draining on her, so she needs some help keeping herself in the form. She's been doing this since before Jazz and Dan/te arrived, but this is the first time the Bats have seen her "sweating" (melting) and Danny helping her fuel back up her core. When Jason gets told this he becomes so extremely smug. Then Bruce realizes, Dani was both the first to come willingly, AND the first to choose a "rider" in Damian.
At first, The Bats can't figure out how Damian could possibly be the rider of "Pestilence" but Tim, in his studies, realizes that the commonly known "Pestilence" label for the first horse was a revision to the original Conquest. Dick points out that one of the first things Damian did when arriving in Gotham was try and kill Tim to "claim" his "rightful place" as Robin. Dani might be showing attributes of Pestilence, but she "chose" a "Rider" that has definitely shown the mind and willingness to attempt to conquer.
All of them hear these talks and ideas of course, but brush it off at this point. All of them except Dan/te however. Being the perfect mix of Danny "Stick to the Bit" Phantom and Vlad "I made my Ghost form look like a vampire for the show of it and stuck to the bit even before I knew I had to play it for another half-ghost" Plasmius, decides that, he is totally the Horse of War. Before the Bat's can even think about if they're simply looking too far into this, Dan/te Trots his big red "war" horse self over to Bruce, and plops his head down on him as a very clear "This is mine" gesture.
"War" choosing Bruce shocks the Bats in attendance at first, and they ponder over how that could possibly make sense. Dan/te made that choice because he has memories of Batman fighting so hard and long against him in his own timeline, and he sees no one else worthy of the title of "war" than the one human outside Amity that truly gave him a fight. It's Alfred that points out that Bruce is the one that "started" the "War for the soul of Gotham" when he made his debut as The Batman and that's what convinces the rest of the Bats that this is real, happening, and they're witnessing the omens of the apocalypse. Dan/te is thrilled at their worry and fear about this.
When John shows up, he doesn't even stay long enough to remember that the Bats are worried that the Apocalypse is on it's way. He simply steps into the cave, see's the Ghost King chilling, and gets the fuck out of dodge before he can be suckered into some shitty deal he isn't looking for right now. This, of course, sends the Bats into a panic. The "Occult Expert" who had tricked demons without so much as a single sweat drop was so frightened by the mere sight of the horses that he left before he could say anything past the initial greetings in the manor.
The Bats worry who Famine could possibly choose, and if it would even be any of them at all. a few weeks pass with no "Chosen" rider for "Famine" when Cass mentions that during her time in the cave, whether it be her returning to the cave after patrol before everyone else or simply a night off, she had seen Tim researching what he could for this issue (as well as working on the investigative work for cases) at the Batcomputer and that "Famine" (Jazz) had always been sitting nearby, seemingly just...watching.
Jazz was doing this because she was here to be with her siblings and to have first hand experience behind the mask and psych of vigilante's, and Tim just so happened to be the one in the Cave the most, which made him the most accessible due to his research into the issue. This "Choice" is a pure coincidence, but the Bats paranoia don't let them see it as a coincidence at all. They rationalize this choice of Rider because Tim has always been the worst outside Bruce at taking care of themselves, and are simply extrapolating that Tims refusal to sleep for weeks at a time is the "famine" Tim represents.
Jazz almost breaks character at this point, wanting to ease the minds of the people her families basically been bumming off of for what's been at least a couple months at this point. Danny, Dani, and Dan/te all stop her, and convince her not to though, as doing this would change the dynamics of what she's been watching and basically completely ruin her study into and any of the data she's gathered about the Psyche's of Vigilante's. None of them really care all that much about her data or study, but they've all decided to commit to the bit now, and are going to drag Jazz kicking and screaming into it.
After the revelation that "Famine" had chosen her "Rider" the Bats worry tremendously about how close the apocalypse is. Everyone in the family agrees that Jason needs to stay as far away from the cave as possible at this point. There's no other possible choice for "Death" than Jason. He's the "Robin that Died". He's the one that clawed his way out of the grasp of death, and the only Bat that will kill regularly and on purpose. Danny agrees with their reasoning, and decides to simply wait until the next time Jason shows up to "choose his rider".
A month passes with no sign of Jason at all, and it's getting really hard to continue convincing Jazz to stay committed to the bit, especially since it's clear that everyone that does frequent the Cave is rather unhappy with how Jason won't even show up for family dinners anymore. The Bats had been working on the families relationship with Jason and had made real progress, but the "Looming Apocalypse" had really stalled their healing journey.
Jazz decides that it's been long enough and that she was going to reveal that this has all been a prank that the other three had decided
to play and had coerced her to go along with when the Bats get back from patrol that night, screw her study and data, she was helping cause harm to this family. Danny, Dani, and Dan/te all convince Jazz to give Danny until the bats came down to the cave the next night before patrol to go out and find Jason, so he can drag Jason to the cave and they could all give the Bats one last spook before revealing the prank. Jazz reluctantly agrees and Danny wastes no time simply flying straight up through the ceiling of the cave to get out into Gotham.
Danny passes straight through the manor, right past where Alfred is. This is another coincidence, but Alfred fully believes that Danny is Death, and he just saw "Death" leave in a hurry. Alfred immediately lets everyone on patrol know that "Death" has rushed his way out of the cave and manor. All of them realize this can only mean one thing, Death is choosing it's rider, and the Apocalypse will soon come. This causes Bruce, Damian, and Tim to start rushing back to the cave, hoping to be able to use the Zeta-tube to simply go to the Watchtower and avoid the start of the apocalypse until they can gather everyone in the JL and JLD to figure out how to put a stop to the Apocalypse.
Jason isn't on Comms tonight, and he doesn't even know what's coming until Danny simply flies onto the roof he's using as a vantage point on a stake-out, and slips under him to pick him up and fly them both back to the cave. Danny can tell where Jason is due to the corrupt ectoplasm in him that is "Lazarus water". This is just another coincidence, Danny's ghost sense leading him to Jason, but Jason is sure that it's because Danny is Death, and he is destined to take the roll of the Horseman of Death. This even "helps" Jason understand why he still has the All-Blades, even if he never uses them anymore. He has them so he can kill all the things that he normally wouldn't be able to.
Jason and Danny are back at the cave before the rest of the Bats are. Jason is visibly panicked, even through his helmet, and Jazz simply can't handle being part of this anymore. She spills the beans to Jason before the rest of the bats arrive, hoping to calm him down. Jason does calm down, and after the shock of it wears of, and hearing from Dan/te how Jason's insistence that the four of them were The four is what convinced Dan/te to "choose a Rider" and keep the bit going, causes Jason to plow straight through the dying panic and building rage, straight into a laughing fit. Jazz is worried at first, thinking this might be Jason having a bit of a mental break at the stress of it all, but Jason puts her fear to rest quickly when he mentions just how hilarious it all is in hindsight.
When Bruce, Damian, and Tim get back, Jazz is the one to tell them that it's all a prank that went too far. Once Jason knew he wanted to keep it going for a little longer and let the others panic a bit more before revealing it, but Jazz put her foot (Hoof, hehe) down and told them as soon as they got out of the Batmobile. After a short talk, many apologies from Jazz, and a rather forced set of apologies from Danny, Dani, and Dan/te, Bruce lets those still on patrol know that there is no Apocalypse, the Alicorn's they've been housing are actually capable of speech, and that they should call it an early night so they could come in and have a long overdue talk with their guests.