I'm pretty sure she doesn't believe him. Tyrion basically told her that she didn't have to, to just do whatever she could to keep a potential ally. It was wholly a political move. And you're right, Cersei and the lot also don't believe in White Walkers, but they're too busy squabbling over each other. Dany is supposed to be the "hero", and she just came off as a major :bou::bou::bou::bou:bag this episode. She expects to be loved when she's done nothing worthy of that love. (And yes, I've admitted before I partially hate Dany because Emilia Clarke can't act and every scene she's in is painful. It's so apparent the skill levels of the other actors and how monumentally she fails to reach those levels herself. Would I like Dany more if she was played by someone else? Probably. Would I like her? No.)
I liked the old switcheroo they did with making Highgarden and Casterly Rock both white and to give you that small moment of throwing you off. A little let down by Casterly Rock after all these years. But Cersei has effectively wiped out Dany's army now, except for the Dothraki. I mean, the Unsullied are still alive, but they're miles away (although people goddamn teleport all over Westeros all the time, so I'm sure they'll be back next episode). She really should have listened to Olenna when the old broad told her to storm King's Landing and be done with it.
Tbh, I was disappointed that it was Bran, and not Arya, that was at the gate of Winterfell. Bran's insufferable now. xD

