brooks, April is tricky -- Spring Thaw time. The creeks are high, and the snow bridges get rotten. Otherwise, I would have recommended snowshoe hiking in the Tetons or the Canadian Rockies.
I think your best bet is going to be the area around Bryce. It is cooler and less busy than the Moab area, it is not too far away from your home, and there is a lot of great boondocking and camping. Kodachrome State Park, not far from Bryce, is great, too. Both of them look just fine with a dusting of snow. Here is a blog link that you may find helpful:
Kodachrome and Bryce in Cool Weather