Depends, a bit, on how you intend to watch the aurora: i.e. from an organized tour, from a lodge in the area, from a car traveling the highway?
Depends, a lot, on where you'll be going: If it is into the interior of Alaska (i.e. Fairbanks and nearby), you might see some seriously cold weather (-30 or colder)in the winter. In the banana belt around Anchorage and nearby, you are likely to see between +15 to -20 unless its warmer (that has happened a lot recently). Easier to get away from the light pollution in the Fairbanks area than Anchorage.
Also depends, a bit, on the level of activity. Presuming you're going to be just standing around, big down parka, down pants, good headgear (lots of choices, I carry a fur hat in the airplane in the winter for a variety of reasons) and wool/fleece gloves inside big mittens.
If one is going to be standing around watching in -30 weather, you'll want (IMNSHO) bunny boots: double layer rubber insulated boots. If you'll be moving around much, LaCrosse, Salomon, and Keen make boots allegedly suitable for cold weather.
If you're into photography, I think you'll want some very thin gloves in addition to the wool gloves and mittens. I've never found a way to avoid cold fingertips when photographing (or trying to) the aurora.
