Yeah his Speed is only 50 so that leans even further towards Avalanche (especially as he can learn Bulk Up) but according to Bulbapedia he can't learn TM72, which was Avalanche in Gen.IV... obviously just because Avalanche was TM72 in Gen.IV doesn't mean it will be in Gen.V as well, but most TMs kept their number from last Gen...
In short, unless that unrevealed move is a good Physical Ice-type move, it's looking pretty bad for Tsunbear! To cover his weaknesses he'd need something like:
Brick Break (for Steel/Rock)
Aerial Ace (for Fighting)
Dive (for Fire)
Swords Dance
EDIT: Plus, Tsunbear doesn't learn any of these moves through level-up, so that's four whole TMs used on him (which actually isn't too big a deal seeing as they're re-usable nowadays).
But seeing as Dive kinda sucks (even with its power being raised to 80) he'd be better served with a decent STAB move like Ice Punch and hoping that any Fire-types he comes up against will go down to Aerial Ace or Brick Break, in my opinion.
So, like I said, here's hoping he has some good breeding moves! I'd hate to see another Pokemon I really like go the way of the Flareon...