score:3
Yellowstone "closes" on 31 October, in that they cease visitor services and road clearing. The park roads remain open for visitors until the first snow storm that produces enough snow to close the roads. The majority of the park remains closed from that point until mid-December when it re-opens for winter season.
The only access to the park in November, once they close the roads, is the road that traverses from the north entrance to the northeast entrance (Gardiner to Cooke City). That road is the only winter access route for residents in the Cooke City, Montana area so it is maintained year round.
Along the Gardiner to NE Entrance you could see the Mammoth Hot Springs and Terraces, perhaps wildlife in Lamar Valley. But the majority of thermal areas (including Old Faithful) in Yellowstone are in the area that is closed in early November.
The west, south and east park entrances (West Yellowstone, Jackson Hole and Cody respectively) are closed at the same time as the roads. So legally you can't enter through them even on skis or with a snowmobile.
All the above is for doing it yourself. Tours through the park cease in October and don't resume until the winter season.
Upvote:2
The National Park Service has a whole page on Visiting Yellowstone in Winter:
Every year, beginning in early November through mid-April, park roads are closed to the interior of the park to prepare for the winter season which begins mid-December and ends mid-March. This means the only way to visit Old Faithful and other interior attractions in the winter is by snowmobile or guided snowcoach that follow the park roadways.
So yes, it is possible, and that page has much more information and links to services.