I've snowmobiled in Yellowstone N.P. several times, but the last time was a few years ago.
I know the rules have changed considerably and are a "hot button issue" with many politicians. For a while it seemed the rules were changing yearly. I suggest you contact the West Yellowstone (Montana) Chamber of Commerce. The winter economy there depends on snowmobiling and they will know what the rules are for this season.
For those who have never done it, it's definitely something worth putting on your bucket list. The snowmobiling in the park is fairly mundane. You must stay on the groomed trails and abide by the posted speed limit (it's enforced). But the wildlife you will see is impressive!
