Steffie, that snow will help. The cold would send any animal looking for a warmer place--but they have to eat, too. Be sure that there is nothing edible in the basement that is not in a glass or metal container. Since the wind has died down, it seems, watch for tracks. You might even let the dog into the area where it was sprayed again to see if it looks like the skunk is still there.
And, for what it's worth, the law in Michigan is that a live trapped animal has to be released on the same property it was trapped on. Your township or county will have an animal control officer that will trap it and be able to give you more specific instructions.