Sansa has never seen a White Walker or a wight. Until she reunites with Arya and Bran again, she’s never seen anything even remotely “magic” with her own eyes. But when Jon tells her about coming back to life and the threat beyond the wall, she believes him.
“Where will you go?” - Sansa believes, understands, and supports Jon’s plan to leave the Night’s Watch after being KILLED by his brothers. She isn’t questioning his word, she’s wondering what’s next for him (and also a little worried they will be separated again, though I think this is more her being non-assuming than truly afraid he’ll abandon her).
“How many Wildlings did you save?” - SAVE. Not, let through the wall. Jon told her about Hardhome and she believes him.
They may not have had many explicit (on-screen) conversations about the AotD, but she actually mentions it several times.
There is this one explicit conversation, although GA usually just dismisses it as another argument:
“You’ve been so consumed with the enemy to the North you’ve forgotten about the one to the South.” She’s acknowledging the enemy is real.
::Jon Snow voice:: It’s always been real.
They aren’t arguing about whether the Night King exists, but about strategy. Also, even though Littlefinger makes the same point to her later, she responds by backing Jon.
“The Northerners are all facing North.”
Earlier in this same episode, during a different “argument” she acknowledges the threat of the dead again. She doesn’t want the castles torn down.
Which war would that be, Sansa? Oh, right. The Great War.
People are so focused on Sansa being a bit argumentative with Jon this season that they fail to see she’s actually 100% on his side. And btw, I’m glad Sansa argues with Jon and “annoys” him. She’s been through some SHIT and this is the first time she’s felt safe enough to drop the false courtesies and speak her mind, even in frustration. It shows trust in Jon.
Later in the season, she mentions the Great War again with Littlefinger. When they discuss Arya finding the letter, she explains to him why she’s worried saying, “We’re asking 20,000 men to fight with us in the worst winter any of them have ever seen.”
Gee, Sansa. What do you mean? Oh yeah, there’s an army of dead people on the way.
Again, Sansa doesn’t need proof. She doesn’t need to see it with her own eyes. She believes him and spends ALL of season 7 preparing for it, while still finding time to run the North, rebuild her family, maintain Jon’s army, and outsmart/execute the biggest schemer on the show. Which is quite a feat for someone so “useless.”
Anyway… Let’s compare that to the savior.
When Mel first tells Dany about Jon, some interesting things happen. First, Mel tells her about the prophecy, which she immediately assumes is about her.
Dany’s had enough informal education to know what the Long Night means. She wasn’t skeptical of Mel like she was of Jon, even when her advisor warned her (rightfully) that she should be. Still, she hardly registers this part. Dany is more focused on the fact that a stranger has come to tell her she’s special. Something she is immediately ready to own.
“The proper translation of that prophecy would be the prince or princess who was promised will bring the dawn.”
Great, so she’s on board. Ready to take up her savior role and bring the dawn. Only… not so much.
Melisandre tells Dany about Jon, that he allowed the Wildlings south of the Wall to protect them, then united them with the North to face their common enemy. But instead of asking more about this common enemy, she focuses on the fact that she has competition for Supreme Special Savior™.
When Jon arrives at Dragonstone, she seems to have no idea what he’s talking about when he mentions the AotD. Even though the prophecy she was ready to fulfill centers on it entirely, she’s completely dismissive of the whole reason Mel told her to contact him in the first place.
Jon’s credibility is REPEATEDLY shown to her but she still doesn’t believe him.
Tyrion vouches for him with personal experience:
”I liked Jon Snow, and I trusted him.”
Tyrion advises her using logic:
”The reason I believe Jon Snow is because he’s here. All of his advisors would have told him not to come. I would have told him not to come, but he’s here anyway.”
Tyrion even tries to get her to work with Jon for purely political reasons, since they need allies.
Dany’s response? Disrespect, imprisonment, continued demands that he bend the knee.
When Jon shows her the carvings in the cave, which she believes are real, she tells him (quite dramatically) that yes, she will be the savior for him… but still only if he bends the knee. And to be clear, what she means is she will fight for the North AFTER her own war is won.
Then, when Jon gets a message from his brother that the threat is drawing near and time is running out, what does she do? Threatens him again, requires a WHOLE lot of time get wasted by getting proof for Cersei, and still prioritizes her own war first. Even after she sees the threat with her own eyes, and loses a dragon, her war comes first.
Meanwhile, back in Winterfell, Sansa is preparing for the Great War. She is fortifying her home as a refuge for the ENTIRE NORTH. Her focus is on feeding and arming her people, on protecting them from the great threat.
Why? Because “whatever direction the threat comes from,” be it dead men, dragons, or dragon queens, Sansa knows:
So, tell me again about Sansa being power hungry and Dany being the only hope against the Long Night. I’ll wait.