Snowbird & Alta
While Alta and Snowbird are distinct mountains (note that Alta isn't snowboard-friendly, while Snowbird is), the next-door-neighbors offer a joint pass called the Altabird, so it's fun to hit them both on the same day if you can. Alta is Utah's classic advanced-skier mountain, with some of the steepest terrain in the Wasatch—it's here that you'll find a lot of hardcore locals, in part because you can access plenty of backcountry via Catherine's Pass. Snowbird is famous for its aerial tram, which takes you all the way to the top of the mountain in one ride and has stunning views—like Alta, it's also home to some steeper, more advanced terrain than the other mountains in the area. Both of these mountains are excellent on a powder day, but you'll have to beat the locals to get any of the good stuff—expect them to be tracked out by 11am at the latest.
Brighton & Solitude
Located in Big Cottonwood Canyon, Brighton & Solitude (which are separate mountains, though you can access them with one pass if you choose) feel a little less commercial and a little more local than their bigger counterparts in other areas of the Wasatch. It's true that you won't find the same masses of terrain, but you will find shorter lift lines—in fact, this can be a great place to come on a powder day, since you won't be battling for fresh turns with the rest of Utah. Brighton's on-mountain terrain isn't huge, but they've got a great terrain park and an open-bounds policy that makes it remarkably easy to cross over into the backcountry. Solitude has historically been a locals' secret for great powder, and a recent buyout by Deer Valley means big infrastructure upgrades are likely in the works.