When we talk about snow storms, we use only that term - snow storms. They can be big or small, negligeable or "stuck inside for two days" big, but they're all called snow storms. When you talk about wind&water storms, there are a variety of names.

Are there different names for snow storms where you live?

========================================================
LATER EDIT:

Ooops, forgot to add that I was talking about French in the question above.

Doc. Bill sent me a note mentioning Blizzard, Arctic Cyclone, and Whiteout. Ooo, and Nor'easter.

I particularly like the term whiteout. So snowy that you can't tell where ground ends and sky begins.

I'm surprised that we don't have that in French. Instead we'd say "it's a storm where you can't tell where ground ends and sky begins." A bit long, no.