Anchorage in the winter is tons of fun, but keep in mind that the days are short and the weather can be pretty chilly. If you like sporty things, there are fantastic cross country ski trails all over the city, some are lit for evening skiing. You can ice skate at Westchester Lagoon. You can hike up FlatTop or walk the trails at Kincaid Park. Tons of stuff to do to burn of your Christmas feasting. If you're not sporty, you can check out the Alaska Native Museum or wander around the lobby area at the Alaska Native Medical Center to check out the fantastic displays of Native Art (the gift shop is fantastic too). There's a decent art museum downtown if you like museums. Have a great time and dress warmly!