Actually, it's a very good idea to specify where you'll be backpacking because any intelligent responses must be tailored to the location in which you'll be. Note W_D's post about the different parts of Utah! It's important to tailor the gear you take to the environmental conditions you'll encounter.

I really don't have much to add to W_D's post. She has spent a lot of time in Wyoming's Wind Rivers, very similar to the Uintas, while most of my experience has been in the northern Colorado Rockies and the Pacific Northwest Cascades. Really, not much difference, although the weather in the Cascades is usually (although definitely not always!) a bit milder than in the Rockies.

My main memory of the High Uintas (from age 11) is waking up in the middle of the night with my parents turning the tent around (with me in it) because the storm (a 3-dayer) suddenly started blowing from the opposite direction, right into the tent door.

If possible, drop down to timberline to camp. If you can't, then at least get to a lower elevation (not on a ridge where the lightning is more apt to strike) and make full use of any wind protection provided by krummholz (which, when I was a youngster, we called snow mats).