1

Never staid in that region in a hotel, but booking.com/TripAdvisor should be able to give you plenty of ideas. For example: http://www.booking.com/hotel/fi/ukolo.en-us.html

Be fast, though, for Christmas.

2

Well, except in Saariselkä. Might be an option as well, although far from serene.

3

How flexible are you on the location? Similar igloo experiences can be found at least in Kiruna in Sweden and Alta in Norway. However, as you had checked the log cabin options from Kakslauttanen too, I assume you want to find accommodation nearby. Kakslauttanen is close to a ski resort (Saariselka) as mentioned. I'm sure you'll be able to find hotels with vacancy for your dates (not igloos unfortunately) still. However, if you don't do skiing and aren't going to need any nightlife, there's always an option of going another 30km further north to Ivalo which is a nice little town with at least two decent hotels (Hotelli Ivalo and Hotelli Kultahippu).