This is an interesting ask, but unfortunately also one with a lot of unknown variables... I will divide this long reply into chapters:

Characterization of Domeric

We only know little about Domeric’s personality. We know that he was a “quiet boy”, very talented with a diverse array of hobbies. We also know that he was friends with Lord Redfort’s sons, implying that his quiet personality doesn’t translate to him being a loner and that he has a social streak to him - he also later wants a brother by his side, so it seems he was lonely in the Dreadfort and craved company.

In the Vale, Domeric had enjoyed the company of Redfort's sons. He wanted a brother by his side, so he rode up the Weeping Water to seek my bastard out.

We know nothing about Domeric’s feelings about the Starks. He was born and raised a Bolton, who historically do not have the best relationship with the Starks; despite Boltons bending the knee to House Stark, we do not have a recorded marriage between the two houses. However, Domeric spent 4 years as Lady Dustin’s page and 3 years at the Redfort, opening up the possibility that his values might not have been entirely influenced by Roose (similar to how Ned got an education in honorable values through Jon Arryn). Barbrey is known to despise the Starks, but was also Brandon’s lover and is shown in aDwD to still have fondness for him, so it is unsure which values she might have imparted on Domeric.

Domeric is said to have been a good jouster, and enjoyed the company of his friends. He might have liked being part of Robb’s honor guard, which has at least several characters that seem to be around his age (i got the impression it’s all young people, like a squad for Robb).

While we never hear about Domeric being cruel or unlikable, we also have to take into account that most of his descriptions come from his own father talking about him, who has reason to concentrate on the positive aspects. Barbrey seems to have loved him, but she is also his aunt, and since her positon as Lady of Barrowton forces her into being an eternal widow, she might have seen Domeric as a son of sorts, so she would have been biased. We also know he was good friends with the Redforts, so he probably does have charme to his personality and does not present himself in an unlikable way. However I do not think this necessarily has to translate into him being a good person or a “cinnamon roll”; there’s plenty of characters in the books that are well liked and charming but still commit war crimes and other cruelties.

Relationship to Roose

Roose never makes a direct statement about his relationship to Domeric. We know he took care to give him a good education (music, histories, and fighting are mentioned), and he sent him to House Dustin and House Redfort to be fostered which is a great opportunity for a young Lordling to forge connections. 

I believe Roose expresses fondness for Domeric in the way he talks about him; He mentions him and then launches into a long reminiscence without much of a reason (thought granted that is pretty much the theme of that chapter), he proudly mentions all his talents and how gifted he was, and seems to talk with a certain sadness/bitterness:

Now his bones lie beneath the Dreadfort with the bones of his brothers, who died still in the cradle, and I am left with Ramsay.

Horses … the boy was mad for horses, Lady Dustin will tell you. Not even Lord Rickard's daughter could outrace him, and that one was half a horse herself. 

Unfortunately that doesn’t necessarily need to translate back into Domeric being fond of his father - We can compare this to Roose’ relationship to Barbrey, where he seems to put trust and effort into her (”How many of our grudging friends do you imagine we'd retain if the truth were known? Only Lady Barbrey“ | “[Roose] takes care to keep me sweet”), while she on the other hand talks in a very disillusioned way about him (”Roose has no feelings, you see.”). We do know Roose appears to be the only Bolton (besides Ramsay), so the lonely Domeric might feel attachment to him in that aspect. Roose is generally liked by few characters, and often appears cold and unfeeling. He is deeply flawed, has a mean aspect to his character (like his mean sense of humour), is mocked for his strange health habits, and seems to talk a lot and think hes very smart and witty. On the other hand he is also somewhat tolerant/laissez-faire (”Your amusements are your own, I will not chide you on that count”), he seems to have provided Domeric with everything he could want and supported all his hobbies, and judging by how Walda seems to like and trust him (”Lady Walda gave a shriek and clutched at her lord husband's arm.”), and he also doesn’t agree with Ramsay’s treatment of Jeyne ("Roose is not pleased. Tell your bastard that."), we can assume that Roose does not treat his family members in a cruel way. It is also worth mentioning that his cold and unfeeling attitude seems to be at least partially motivated by him trying to hide his intentions in fear of them being used against him (in line with his other cautious behaviour), so it might very well be that he is warmer towards people he trusts (Note that we only ever observe him from the PoV of people he is not close to). So while there is a lot to dislike and be annoyed by about Roose, he also has qualities that Domeric might have liked.

It is interesting to analyze the scenes with Roose and Ramsay for how he might have interacted with Domeric. We know Roose loves to educate Ramsay on how to be a good Lord and impart his wisdom to him, and that he also frequently enrages Ramsay with the tone he uses. The quote “I forbade it, but Domeric was a man grown and thought that he knew better than his father.” suggests to me that he might have butted heads with Domeric in a similar way, giving him advice that Domeric doesn’t always listen to. Since Domeric openly disobeyed Roose, it appears he was not scared of his father, and that he had a proud/stubborn aspect to him.

It is of course also important to note the differences: Ramsay is of a lowerclass background (Roose has been shown to be classist - “His blood is tainted, that cannot be denied.”); He has a cruel und unwise personality that might frustrate Roose and make him resort to using a meaner tone with Ramsay; and we know Roose on occasion talks negatively about Ramsay when he is not there (”Ramsay's nature was sly, greedy, and cruel. I count myself well rid of him.“), though he has also talked positively about him in related scenes (”Yet he is a good fighter, as cunning as he is fearless.”). While he talks in a condescending tone to Ramsay and even insults him, he might have had more of a respectful tone to his competent, trueborn son.

Domeric and the Red Wedding

I think in any case, Roose would have tried to take care to keep Domeric out of any great danger. Domeric would have surely argued with him on many points (”Domeric was a man grown and thought that he knew better than his father“), and since he seems to have had martial prowess he would have probably insisted on participating in battle. If Roose had tried to participate in the Red Wedding without Domeric’s knowledge, Domeric would have probably been a nuisance; he appears to be highly intelligent, he has no fear of speaking out against his father if he doesn’t agree with an idea, and he doesnt seem to blindly comply with his fathers wishes if he doesn’t see a reason to. Roose would likely not have let him near a situation as dangerous as the Red Wedding especially if Domeric doesn’t know about the plan, but it might have been hard to get him out of the way without a good reason.

If Domeric knew about the Red Wedding, he would be a good asset, since he’d likely have a position close to Robb (as i mentioned the guard seems like something he’d participate in). However even in this case I think Roose would have tried to keep him out of the Wedding itself, as not to put his sole heir in danger.

However, another problem is that not only does Roose never state his precise list of reasons for the red wedding (making it a point of debate to discern what exactly changes if you change the course of events), according to grrm he also wasn’t even completely set in his tracks to go through with the Red Wedding until pretty much the last minute:

As for Bolton, if you reread all his sections carefully, I think you will see a picture of a man keeping all his options open as long as he could... sniffing the wind, covering his tracks, ready to jump either way... even as late as his supper with Jaime at Harrenhal... - SSM 8/3/2000

Domeric’s presence could influence so many plot points it is hard to say if Roose would have even come to the point of getting the Red Wedding in motion.

Would Domeric even go to war with Roose or would he stay behind as Castellan of the Dreadfort like Ramsay did? Is Ramsay even still there/does he still have a position of power or role in the story? If Ramsay isn’t there do Bran and Rickon even flee and get presumed dead? If Bran and Rickon are still alive does Cat still free Jaime and commit an unpopular political decision? Does Winterfell still burn? It doesn’t seem likely that Roose instructed Ramsay in the minutiae of what happens in Winterfell considering Ramsay is presumed dead before he even enters it; So would Domeric in charge of the Dreadfort have instead opted to liberate Winterfell if someone reached out to him? Note that the disaster at Winterfell seems to be one of the main reasons that Roose considered the Red Wedding:

"I [serve] the King in the North. Or the King Who Lost the North, as some now call him.“ - aSoS, dinner with Jaime

"What … what do you owe me, m'lord?"   -   "The north. The Starks were done and doomed the night that you took Winterfell." He waved a pale hand, dismissive. "All this is only squabbling over spoils."   - aDwD, dialogue with Theon

Also with a trueborn and gifted adult heir, would Roose even have considered marrying a Frey maiden? Would Domeric have wed one instead, or would Roose prefer a better alliance for him? Would Roose marrying a Frey count that much for an alliance if the Frey child wouldn’t even inherit the Dreadfort?

Conclusion