We just got back from a mighty 5 trip. We absolutely loved Canyonlands, Arches and Capitol Reef (don't skip that one, most people do, but it was such a lovely place, not crowded at all, and our hikes were quiet and beautiful). Bryce was gorgeous with the snow, we did the Queen's loop, rented crampons from Ruby's inn for $10, they helped a lot. But most of the ice/snow will probably melt by next week, so you might not need them. Although the crampons also helped with not getting our shoes and pants muddy with less splatter. We had trouble with parking at one spot in Bryce, but the shuttles hadn't started then, you hopefully shouldn't have trouble next week. I wasn't impressed with Zion, the crowds were too much for me. The lines for the shuttle were long, but they moved really quickly, by the time one shuttle loaded, the next was already waiting.
My biggest recommendation: Download the gypsy app, we all loved it. You can get a bundle for all 5 parks, it was worth every penny.