There is Christmas all year long at the North pole with the Christmas shops and visits to Santa. Fairbanks is a decent sized city, not as large as Anchorage, but has enough things to do that you're not bored. On the long winter nights, you can see the Northern Lights and a sky that does not end. The mosquitoes can be so thick you're afraid to breath. The best time to camp and avoid the flying pests is in May and September.
Fishing is fantastic, but expensive for non-residents.
The salmon is great smoked and then frozen for use all year long. Bears are everywhere. It was a shocker the first time I stayed in a camp ground with a bear trap at the entrance to the campground. The bear trap was a huge barrel with a trap door at the end.