I was worried about that, maybe i should just let the character specialize on all destruction magic. But give him/her a ''cold'' appearance like a pale skin and white hair. And then ice magic would just be the main spells the character will use, yet he/she does know as much about fire and shock magic.
That would be best advised. Everything in skyrim is resistant to cold. Ice Wraiths, Frost Trolls, Falmer, Ice Wolves, Snow Bears, Nords, Draugr, Wisp Mothers, Dwemer Automatons, Necromancers, Mammoths, and of course Frost Dragons