A light blowing swirl of snow that's just barely falling is a flurry. There might be a brief flurry or two at the beginning of the winter, with no real heavy snow until January.
You can describe a snow flurry, or a similarly swirling flurry of leaves or papers. When people act this way, rushing and fussing around, that's another kind of flurry. There might, for example, be a flurry of activity in the morning at your house as everyone hurries to get ready for the day. This sense of flurry is actually about a hundred years older than the snow meaning, which was first used in mid-1800's American English.