Yellowstone is great if you want to see wild life and interesting geology. As far as the snowmobiling goes, it's really just a mode of transportation within the park. You're not allowed to leave the road and if you're turning around you have to do it within the road. Considering that. I would just take a ride in one of the snow coaches to enjoy the scenery from a heated more comfortable seat. On top of that almost any piped sled exceeds the noise limit to ride in Yellowstone.
If it's the snowmobiling you want then spend your time in Island Park. You can pretty much ride whereever you want. There are groomed trails to travel around on, the ranchers lay their fences down and you can ride across the fields and play in the powder.