The town of West Yellowstone, on the edge of the national park, is home to some of the best snowmobiling in America. Most hotels in town rent snowmobiles ($120-160 per day depending on if you want heated hand warmers, bigger engines, etc) and warm clothes ($15 per day for gear including boots, mittens, helmets, snowmobile suits, face masks) necessary for chilly days dipping below zero.
Perhaps the most famous trail is the 28 mile loop to Two Top Mountain. Heading west out of town, the trail snakes through forested scenery, along a frozen river and up, up, up to a winter wonderland. Snow encrusted trees take on shapes described as frosty guardians, snow ghosts, and fantastical snow creatures that stand alongside arches and snow caves created by heavy snowfalls.
And if this isn't enough to lure you here, the surrounding views should. Panoramic views of mountains covered in snowy trees extend to three states: Idaho, Montana and Wyoming. On a clear day you can see the Madison River Canyon in Yellowstone National Park, and even the Teton Mountains.