This is something random I found that may explain a few things:
http://scienceray.com/biology/zoology/c ... ic-tundra/ :B
Lions can
live in snow but not survive, if that makes any sense. Their bodies are built for surviving in the hot African plains, but that doesn't mean they will drop dead the instant they make contact with snow. It's just that in the long-term, lions are at a much higher disadvantage than other predatory animals that live in cold climates, because of their different evolutionary traits (fur color for camouflauge, amount of fur, etc).
To make your fanfic more realistic, a lot of lions would have to die of cold/hunger/other issues, but lions are tough animals, and I'm sure more than a few could survive snowy conditions for a while. Hunting the different type of prey would have to be something they overcome, and I imagine other predators such as wolves and eagles would compete for resources.