I LOVE cold countries and snow for holidays and been a few. I'm a big kid!
Agree with tigerlilly. No where has been as christmassy as Copenhagen.
Christmas in a box as you imagine as a kid is Tivoli Gardens. The decorations, the rides and the atmosphere. You won't get snow, but you don't need it.
And for the grown ups the christmas beers are out of this world. Just only go for a half or you'll be staggering (they are 10% as it is!!!). We went to Copenhagen between christmas and new year. If you go to Germany I think a lot of places have finished by then. Depends on where you go.
Iceland is fab. Reykjavik is a lovely little city. Theres plenty of little things to do (Blue Lagoon, lots of waterfalls, whale watching etc) plus european christmas market. Its hit and miss with snow around christmas. You might get it, you might not.
I got married in Swedish Lapland (Icehotel). The food was pretty much a choice between reindeer (or moose or elk), lingonberrys (little red berries) and fish. I love reindeer - its like venison - but after 4 days of huge meat chunks, your guts start giving a protest. They do have other stuff but it seemed fairly limited. It was an amazing place, and we got to go husky dog sledging (NOT CHEAP) which was brilliant, but stinky and not too children friendly. I believe some of the other Igloo Hotels in lapland though. There is a couple in Finland which are cheaper, such as Roveniemi mentioned above. (You usually stay in warm rooms for all but one night - trust me as amazing as it is, you only need one night!). Of course you are guarenteed snow.
As for daylight hours. The lack of daylight wasn't a problem but does mess with your body clock. 4 hours of daylight is weird. You are unlikely to go too far north anywhere in Lapland that gives you much less than that. Its enough time to do a daytime activity but there are things you can do in evenings as they are geared up for the lack of light. The thing you need to watch out for more in Lapland is the temperature. At the Icehotel it dropped to -19C at night. It is a different kind of cold though - a dry cold not a wet cold. So it doesn't get in your bones. Just wrap up well. The Icehotel provided clothing free of charge - I don't know if other places do too.
Its worth knowing that 2012/2013 is a solar maximum. This means its a really good time to head to Iceland & Lapland (either Norway, Sweden, Finland) or to Canada. You have the best opportunity in 11/12 years to see the Northern Lights. If thats not Christmassy, I'm not sure what is!
As for dates, it depends on where you go. 25th Dec is generally UK, but everything is still closed in Europe. Normally it seems to be 6th Dec (for kids) and 24th (for family) but it depends on country. Unless you are at a resort, don't expect much to be open 24th/25th Dec.
Talinn is next on my list for next year. I've hear some amazing stuff about the place AND ITS CHEAP. They should have snow by Christmas time at least. Its a little too south for Northern lights though.
Lapland (especially Norweigian Lapland) is horribly expensive. Iceland is reasonable at the moment. Switzerland is horrendous. Don't think Austria is great either.
Sadly I can't give you any information about Austria or Switzerland, but I think I've probably just rambled on for long enough anyway!!!!