The closing dates of campgrounds vary, but you can find the dates here: http://www.nps.gov/yell/planyourvisit/camp...yellowstone.htm
This is the site of Xanterra, the concessionaire running the campgrounds and hotels in the park.
Be careful of planning your visit around the average temperatures for Yellowstone listed on many sites. Variability is the rule rather than the exception in this part of the country. Freezing temperatures at night are a regular occurance already and will become more common with each passing week. However, late fall
and early spring are among the best times to visit the park. Crowds are greatly reduced and animals are more visible. The risks of poor weather are more than offset by the great rewards of the fall
Enjoy the trip.