Jeff,
Check us out rockinmranchwyoming.com. We own and operate a snowmobile rental and cabin rental business 36 miles South of Jackson in Alpine. I am happy to answer questions whether you stay with us or not. I guided in Yellowstone for many years. You can only go through Yellowstone on a guided tour on a park approved 4-stroke. Although there is riding from Jackson, there is more in the surrounding areas, including Alpine, Togwotee, Granite, Cliff Creek etc. If your focus is snowmobiling, you may consider staying in one of the bordering areas and visiting the tourists when you feel like driving to Jackson. Jackson is about an hour from Togwotee and 45 minutes from Alpine.
Good Luck
Rob 307-654-2288