RE: snow in february
Gothenburg has a very "British" climate, being on the west coast with the Gulf Stream/North Sea. This means wet and windy as I'm sure you know. Otherwise, it is a lovely city.
Stockholm is much more sunny and cold and "Baltic/Siberian". But there is no guarantee for snow in either (right now it's 15 degrees here which is way above December average). Having said that, January-February are usually colder. Once it snows, Stockholm is a lot more scenic as it gets colder and not so drizzly snow. There is also all the water around you whilst Gothenburg just has its river. Have a look at my "Fjällgatan" tip on my Stockholm tip which I think is a winter picture.
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