While snowmobiling in Yellowstone during winter is a popular activity, you cannot just show up at an entrance to Yellowstone National Park with your snowmobile and expect to get in.
To go on an unguided tour of Yellowstone, you need to apply for a permit in August through a park lottery system at www.recreation.gov or 877-444-6777. Only four non-commercially guided groups are allowed in Yellowstone per day, which equates to one per park entrance.
Permits cost $40/day and are awarded in September. Any cancellations or unclaimed permits are given out on a first-come, first-served basis starting in early October.
Enter the lottery here.