Here are the "opening dates" for Yellowstone, that I could locate on the national park site.
Where do I enter Yellowstone National Park?
Yellowstone has 5 entrances to the park:
North Entrance - Gardiner, MT, the North Entrance is the only park entrance open to wheeled vehicles all year. November through April, provides access to Cooke City, MT. US Highway 212 east of Cooke City is closed to wheeled vehicles November through April. The Mammoth to Norris road is open to wheeled vehicles from April 20 to November 4, and to tracked oversnow vehicles from around December 17 to March 12. Closest airline service is Bozeman, MT
West Entrance - West Yellowstone, MT, the West Entrance is open to wheeled vehicles from April 20 to November 4, and to tracked oversnow vehicles from December 17 to March 12. Closest airline service is West Yellowstone, MT, Bozeman, MT, Idaho Falls, ID, and Salt Lake City, UT.
Northeast Entrance - Silver Gate and Cooke City, MT, is open year around for wheeled vehicles to Cooke City through the North Entrance. Opening dates for roads east of Cooke City vary from year to year, depending on the weather. The Beartooth Highway is
open from late May/early June to mid October and is dependent upon weather conditions. Closest airline service is Billings, MT.
South & East Entrances - Open to wheeled vehicles from May 11 to November 4, and to tracked oversnow vehicles from December 17 to March 12. Closest airline service to the South Entrance is Jackson, WY and Cody, WY to the East Entrance.
So, unless you have "tracked oversnow vehicle", there won't be any chance you can even enter Yellowstone.
This is not really something that you can see/do during the middle of the winter.
2017 Ford F350 Crew Cab 6.7L 4x4 DRW