We went in early to mid May and the NE entrance was not yet open. They hadn't repaired any of the damaged guardrails on the E entrance that appeared to have been taken out by a small avalanche and there were still snowy areas in the higher spots in the center of the park. We got snowed on in the Tetons but it was very cool as an adolescent moose rubbed up against our RV as he was grazing right outside.
Most days it was flannel shirt or jacket weather.
We went the first week in August last year and the lows 2 nights were around 30. There were some unprepared COLD campers