If you want this to look really amazing, layer a texture over the ground as snow begins to fall.
This texture can be dynamically generated, or prebaked. (Just depends on what quality and performance you want)
As the snow begins to fall, I strongly feel that a glow effect might make it look pretty amazing.
I like the idea of the noise function, but I think it might be better if the snow overlay is generated based off the terrain that it falls on, ie: it clusters on the sides of hills, spreads out on hill tops, etc, etc