National parks and monuments that allow snowmobiling include: Lake Clark National Park and Preserve (AK), Wrangell-St. Elias National Park and Preserve (AK), Curecanti National Recreation Area (CO), City of Rocks National Reserve (ID), Crater Lake National Park (OR), Newberry National Volcanic Monument (CO), Cedar Breaks National Monument (UT), Mount Rainier National Park (WA), Grand Teton National Park (WY) and Yellowstone National Park (WY).
One suggestion would be to call before you go (all numbers are listed in each park's section).