In my opinion, Bryce is most beautiful in the winter with snow, fresh if possible. Of course, you probably already know that sunrise is the best time for photos at Bryce. Bryce usually has lots of snow in winter. Depending on the amount of recent snow, the roads may be open only a short way or they could all be open. Even after a big snow, however, the parks service is pretty good at getting the roads open fairly quickly. If you're up to it, a hike through the hoodos in the snow is beautiful and peaceful since there are likely to be very few people below the canyon rim. Snow shoes shouldn't be necessay as long as you have some decent boots and gaiters. On the other hand, unless there is fresh snow at Zion, I think that winter is the least beautiful time of the year. Same for Canyonlands and Arches and the other parks and monuments in southern Utah. Those areas don't get much snow. If you are fortunate enough to get snow, however, you can get some unusual and exceptionally beautiful photos. In addition, in my experience in Canyonlands and Arches area especially, sunsets tend to be much more colorful in winter. Accordingly, I recommend that you check the weather forecasts and try to find fresh snow, but realize that the snow usually lasts a very short time in lower Zion, Canyonlands and Arches. You may also want to consider more than just one day at Bryce.