Have climbed 10 peaks in this area, a couple more than once. Ptarmigan Peak (9/19/09); Coon Hill, PT 12429 and PT 12336 (10/31/09); Prairie Mtn (12/5/09); PT 12358 (8/21/11); Ute, PT 12358 and Ptarmigan (10/6/12); Williams BM, Williams Peak and PT 11204 (6/23/13). Ptarmigan Peak and the approach trail have excellent views of the Gore Range, as does Ute Pass and Williams BM - highly recommended for the views!
I've done this one a couple of times from the Ptarmigan Trail side. Climbed Ptarmigan Peak but have not yet gone over to Ute Peak. This one's worth it for the panorama of the Gores, but the trail itself is sort of lackluster.
Did this one with Jim (Colonelpyat) on a perfect day in late Jan, 2006. He skied, I snowshoed. He was fast, I was slow. I new the views would be good but I didn't realize the views would be that good! Excellent, and very comprehensive views of the Gore Range from up there, certainly well worth the trip.
My friend Dave and I had a great time on this traverse. We had great views of the Gore as well as down into the Williams Fork draingage. Highly recommended but beware that there are not many bail-out points.
I look directly towards Ptarmigan and Coon Hill from my living room so they are quite familiar.