My wife Penelope and I skied to Cedar Breaks NM from Brian Head in late January 2016. As this was mid-week, there were no other people in the Monument. The winter scenery from the 4 viewpoints along the rim was really great and we had most wonderful 8 miles RT of AT touring. The place is fabulous in winter.
Despite being a Saturday in late June, Cedar Breaks was uncrowded and peaceful. My wife and I did all of the "advertised" above-the-rim trails, including the Ramparts Trail in the afternoon, which we practically had to ourselves. The area is amazing -- walking along the rim and seeing green forests with streams, animals, and flora on one side, while seeing the breaks dropping off on the other side, is an experience unlike any other. I hope to make it back to do an overnighter on the Rattle Creek trail on the north end of the park.
The Alpine Pond Trail in June still had lots of snow. And we really enjoyed seeing the bristlecone pines, even though the older ones are "mostly dead".