Vulpix living on a cold mountain makes sense
If you’re confused about Vulpix’s type/appearance change, check what the official site says
“To avoid the normal habitats of other Pokémon”
Now look at the island with the snowy peak
This island, compared to the others, features many different landscapes:
1. A desert, most likely full of Ground-types, not ideal for Vulpix;
2. Badlands/rocky area, same thing, probably full of Ground and Rock-types;
3. What looks to be a rainy forest/jungle, so again, not good;
4. A swamp, probably inhabited by Water and Ground-types, nope;
5. A lagoon, so Water-types, nope;
6. An icy peak, full of Ice-types. Perfect!
It makes sense for Vulpix to adapt to the cold area, because it’s the one with the least amount of threats. Ice-types, being weak to Fire, are excellent prey for Vulpix.