as for controlling ice... it might depend on how it's flavored or the mechanics on how you wish to accomplish it, like is it of her own power entirely? like it just appears, maybe a bit OP but if it's maybe through Shiron, like due to their bond Shiron's natural affinity for ice type abilities and attacks, I could see it being possible, just wouldn't be as strong or any stronger than the ice type abilities an Alolan vulpix would be able to accomplish. so she could maybe use some of Shiron's ice type (or movesets that Shiron could use) moves but they emanate from her rather than the pokemon, or something similar, but doesn't get the abilities that an Alolan Neintails would have.... at least that's my thought, you could possibly flavor it within reason, or maybe just have it that for some reason sherry is less effected by the cold even more than normal 'the cold never bothered me anyway' kind of deal, maybe even Sherry finds the cold, very cold environments more comfortable? Ultimately it's probably up to the boss with what is feasible or not.