I'll take 2h, destruction, conjuration, restoration, heavy.armor, block, and enchanting. I'll use Stahlrim armor with the mask of duukan. And get the black book for frost breath, and enchants 10% stronger. Any suggestions?

Sounds good! I'll just say that I'd go with Nord for race. They are the most in-tune with the cold, as reflected by their 50% resistance to frost.

Why 7 skills?

8 with Smithing.

That's more than enough, any more and he'll stretch his build too thin.

So what do you suggest?

Nothing, just add in Smithing for Stalhrim and you'll be good to go.

I find battlemages that use Two-Handed to be counter intuitive. I'd figure you'd want to use melee and magic in conjunction with each other, not one at a time.

From what I read, Battlemages use Conjuration and Destruction for range attacks. Then they switch to Two Handed when enemies get too close.

I would go with using magic in conjunction with one handed weapons (Swords are okay, but BattleMages are often portrayed using maces) I recently just finished a playthrough with a battle mage and it turned out great, I had a blast. Got both 100 One Handed and 100 Destruction My favorite was using incinerate, and a Daedric Mace with the Elemental Fury shout for faster attacks to absolutely destroy my enemies from close and far!

Hmm, maybe I'll do a fire Battlemage