Re: Iceland
Nice country to visit in the summertime with great nightlife and great nature (especially if you like horses). But in wintertime it's not really that "Icy". Around new years eve you will probably have more rain than snow around Reykjavik.
And the Ice Hotel; It's in Sweden
What about Cuba. Some friends of mine was there for their honeymoon a couple of years ago and they loved it. Certainly something different.
Or climb a mountain. Equador have some nice, high and easily available peaks. Rest out afterwards on the Galapagos.