I think a 100% safe snow promise is impossible to make for any European city at that time. Sure, here in Sweden we're supposed to have a lot of snow but it's the middle of winter right now and all we get is rain.
If you'd want to go for a cheap city destination than Eastern Europe is definately the way to go. Accomodation and resturant prices are lower as well as the flight fare. However, Bulgaria, Slovenia, Hungary etc. are all down in continental Europe which results in higher temperatures and so decreases your chances of snow.
The snow chances are for sure higher in the Scandinavian countries. But so are the prices!
If you were to drop the the idea of going to a city I think you'd have far greater chances of seeing snow. There are the Italian and Swiss alps. There's the whole of Scandinavia and Balticum + a large part of Eastern Europe.
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