Mirror Lake Scenic Byway

The full Mirror Lake Scenic Byway runs from Kamas, UT to Evanston, WY, driving right across the western portion of the Uinta Mountains. The full route is about 72 miles, but only about 20 miles are in Wyoming. More than half the Byway is in the Uinta-Wasatch-Cache National Forest in the Mirror Lake Area: 320 square miles of high mountains and sagebrush flats, grassy meadows, alpine tundra and heavy coniferous forests, all mixed together with an abundance of wetlands, streams, ponds and lakes.

I don't know about the Wyoming section of the route but the Utah section is closed when the snow starts to pile up (there's a rumor that the Utah section also comes with a small National Forest Service fee attached).