According to 360:

Wyoming:

The crowds are at their largest, and most cumbersome, between the third week in June and the second week in August. September seems to be an ideal month to visit Wyoming tourist attractions, crowds are smaller, the mosquitoes are dead and the weather is usually milder.

Depending on the location you are in, travel weather for Wyoming ranges greatly especially in the high tourist season. In Jackson, the average summer temperature is 65 F, but can go as high as 80. Bighorn, at Burgess Junction, the average July temperature is 55 F.

All of this differential weather is due to the range of elevation in Wyoming. From, the Belle Fourche River Valley in the state’s northeast corner, at 3,125 feet, to summit of Gannett Peak in the Wind River Mountains, at 13,804 feet. The range of temperature is mostly due to the fact that Wyoming is far from any moderating influence of oceans.

If you are planning on backpacking or seeing the Indian Reservations early/late autumn is the best time visit Wyoming. A major Wyoming tourist attraction is skiing at the Jackson Hole mountain resort. The resort opens for skiing late October and remains open until early March.

This is ideal for the skiing or snowboarding enthusiast, because you get the experience of the Grand Teton vast hills and expertly crafted ski courses. However, Wyoming weather can be tricky in the early spring. One day you experience mild temperature and full throttle sunshine, within 24 hours you a caught in a massive down pour. So if you plan to go in the early spring, you may want to watch for drastic day-to-day changes in weather.

When visiting Wyoming tourist attractions you will soon realize that depending on what elevation you are at it could be a mild 70 degrees to a freezing 30 degrees. In general, early autumn is the best season to do all things in Wyoming and the easiest way to avoid the massive crowds.