TBH, the "scientific" explanation of the White Frost with the axial tilt of the planet causing polar caps to grow and reflect more and more sunlight away from the planet, thus making it colder and making the polar caps grow even more is... suspect to say the least. I think Sapkowski overdid it with this stuff.
Yeah, it doesn't make much sense, and his "scientific" stuff generally feels a bit out of place. He injects modern elements into the universe quite often, but this particular aspect never worked for me. Still, based on the books it seems like it was intended to be the "canon" explanation for this stuff. I wonder if there are any interviews about this subject (although I doubt he'd give a satisfying answer to anyone anyway, being the way he is...)
However, the White Frost was always depicted as the doom of one particular world, and not of the multiverse.
I think it's depicted as being an inevitable end for all worlds, just that it's not some universal event that takes place everywhere at the same time. It's a bit hard to keep track of it because most of it is so vague (intentionally, I guess) and because there are so many different interpretations of it, both in the books and in the games.
I was under the impression that as a Child of the Elder Blood Ciri was somehow tied into the White Frost
It is plainly obvious the first time you hear Ithlinne's Prophecy. It's the head-to-head-combat-against-snow part that is the problem, even in the case that it was meant to be symbolic rather than something to be taken literally.
I would've preferred if they'd just dropped the part where the world is literally ending and made the last scene something more grounded and character-focused. The last scene is ultimately about the relationship between Geralt and Ciri, the daughter finally "leaving the nest" and starting to make her own decisions, with Geralt or anyone else no longer having control over her*. It could've simply been about Ciri going away for an unknown period of time to learn more about her powers or something like that, and I would've had no problems with it. Instead, they just had to put saving the world in there somewhere, as if she wasn't special enough already.
* Because of this I also consider the Empress ending to be a "better" ending than the witcher one, at least if you ignore the books and go with what the games tell you about Emhyr and Nilfgaard.