Where would you like to travel in late December and why?
Home, to my parents. And be able to see my sisters, cousins, aunts and uncles. That is without a doubt the place for Christmas in Europe, if not the world! Unfortunately you're not invited unless you can find a way to become a part of the family… Maybe not the answer you wanted to hear, but the truth! :-)
On a more serious note. More or less every city in Europe offers what I think you are looking for. If they are too cold or not depends on what you consider too cold. But how we feel depends not only on the temperature but on other factors as well. E.g. you will feel colder if you are wet. That also means that a few degrees below zero often feels warmer than a few degrees above zero.
If outdoor markets are important, London is not the best place though. The Chrismas markets are a German tradition that only recently arrived in the UK. So in my opinion the markets in Germany are in a different league compared to the ones in the UK, that tend to feel a bit "commercial". But you can find great markets outside Germany as well. Often people focus on southern Germany, which is a great place. But there are lovely places in the north that tend to be a bit forgotten in comparison, Lübeck e.g. has a great Christmas market and is overall a charming place for Chrismas.
One thing you need to remember is that many countries more or less shut down over Christmas, no open shops or restaurants, no public transport etc. How much and for how long depends on the country. If you want to avoid that you can go to an orthodox country that celebrate Christmas in January. Estonia and especially Tallinn is in my opinion a a good choice, they are majority orthodox but with a large lutheran minority so you will not feel out of place for celebrating i December. Lviv is also often mentioned, a really beautiful city.
