Your thoughts on driving to Yellowstone in winter?

Just to confirm EV2's statement about the roads in Yellowstone, not only is it true but so are all camping facilities. Schedule for shutting down the roads and opening them again in the spring are flexible and depend on when the storms hit.

There is one facility open all year and that is the Snow Lodge as it's called. I has almost everything you need and is next to the Old Faithful Inn.

Look up details on the NPS webpage for Yellowstone.