My 2 cents

I have never been to Yellowstone in the winter. However, a friend of mine works for a natural conservatory organization and she goes there all the time. Based on her:

1. Only portion of the park (from Cody to Mammoth) is accessible by car, if weather permitts. You need good traction tires/chains.

2. Bears are hibernating but there are tons of other creatures, in particular hoof animals. Reason is that they come down from higher elevation to find food.

3. You can rent snowmobiles, especially good for wolf watching.

4. Few toursits.

I think it will be a remarkable experience.