It shouldn’t be too bad in September,but,it can change quickly. I did the tour about a month later in 2011,the Wyoming tourist office thought that it might be snowy and cold at that time.It was cold at
the start,but,the further south we went the warmer it got.The only snow was the night before Yellowstone,but,it wasn’t heavy enough to stop us visiting the Park,it was worse towards the Grand Tetons.We stayed overnight in West Yellowstone,and by the time we completed Yellowstone,the road south had cleared.It was strange seeing snow/frost around Old Faithful.
Most of the tour is about 10,000 feet above sea level,so keep hydrated.