As you can see at the bottom of this official national park link, the roads will close by early November. If you can get to Yellowstone mid-October that would be great. We've been there at that time and had wonderful weather but as you know, you just can't count on the weather. It can snow at that time, also.
If this is a definite time for you to travel, I would just keep a close watch on the weather as you travel and be prepared for Plan B. If you can, adjust your trip to an earlier timeframe. Good luck!
Park Roads - Yellowstone National Park (U.S. National Park Service)