Welcome to FT!

I think the best advice is to plan for layers. Chances are you'll have rain for one or more days (maybe 8 or 10 ) so having some kind of rain jacket that you can wear over a variety of tops - shirts, sweaters etc. - makes the most sense. I'd pick some sturdy walking shoes or boots if you plan on walking on trails, and make sure they're waterproofed or water resistant. For Fairbanks and Anchorage, dress casually as you would in any other urban setting. You're not going to get winter conditions except possibly at very high elevations.