Well..... no snowmobling with the bison at Yellowstone LOL. You have to get one of the self-guided 4 passes issued each day (one at each of the 4 entrances each day), or ride with an escort (reeeeally boring). And in winter the bison 98% move to lower levels, mostly on the north end of the Park. We had a self-guided pass for 2 days last season.... We went down the east side, and the best scene was the Yellowstone Falls all frozen up. he rest was mostly lots of long miles droning along at a 35 mph speed limit and little in the way of game; it was kinda boring. It would have been better to go down the west side where the big geyser sites are, but we all came down with the flu on day 2 LOL and missed that. Summer was honestly better in Yellowstone..
Now Togwotee Pass in Wy and Island Park ID are great. We spent 2 days at Togwotee and just scratched the surface of the trails, never mind the off-trail riding. Elevations of 8000' to well over 9000'. There is a lodge with gas station and restaurant right there and you ride right out of it onto the trails. We have not been to Island Park yet but the pix are pretty dramatic, tons of trails, and an average annual snowfall of close to 200".
We also spent 2 days in the Bighorns. Stayed in Sherdian WY at a nice motel where my wife could relax. Lot of trails, some of them pretty darned fast and some twisty. At the west end, there is a view where you can see across the central basin of WY and to the Absaroka Mtns which form the eastern rim of Yellowshone.... that is an 80-100 mile view.