As you say, "snow refers to the white stuff on the ground;" or "snow" as you say is the white stuff on the ground while that white stuff that appears on the ground in winter is usually snow.

Yet 'snow' refers to the name we use for the white stuff on the ground while the white stuff on the ground is apparently snow but 'snow' also refers to other white stuff that can put one on the ground.

I'm snowed, I think I'll go get a drink...