I've been sportsfishing in Alaska many a time, May-Sept. I would guess that there's no salmon to be had in December (thus no river fishing). I would also guess that the halibut are still out there, but that the seas will be too rough for sports fishing.

I have been in ANC in December, and it's not all that cold, and is a real city with nice restaurants etc. I suspect that there's a web site that lists activities etc. have fun.