It is already in the upper 20's some nights (check Weather.com). The passes are likely to be closed by the time you get there and construction on Norris-Madison will have that closed.
You will probably want to stay at Madison for the North part and maybe even West Yellowstone for the South. (We are not big fans of Grizzly, but most people seem to like it).
The last time we were there in the Fall, we got 6 inches of new snow on October 12 and the only way out from the Old Faithful Lodge (we didn't have the trailer with us) was through West Entrance and back down through Idaho to Jackson. Some of the other roads were not plowed for a week.