The road east of Ten Sleep goes thru a high mountain pass and was very snowy when we went thru west to east last late September. Cody thru the park on 14 was also high altitude and actively snowing hard and being plowed at the time. The hot springs at Thermopolis were a major disappointment, concrete pools inside a building.
So be prepared for weather in the park. Of course I have been in snowstorms there in July. The park is high altitude 9000ft more or less. Cody rolls up the sidewalks at the end of September and all the RV parks close. Be sure to visit Lamar Valley if you want to see critters.
I could not believe the prices at Fishing Bridge now.