Not considering some freak weather phenomena, Zion travel should be OK. Snow should stay above the 7000ft elevation. Most peaks in Zion are about that and the canyon floor about 4000ft. Interesting...private cars are allowed on the Zion Canyon Scenic Drive weekdays in Nov. and later. I thought only shuttles were allowed year round.
Bryce will be different. The rim is in the 8000ft. elevation range. It stays so dry out west, moisture shouldn't last long, but it's 20s F most nights now.
Arches, Canyonlands and Dead Horse Point should be good traveling....4000-6000ft and your really in the high desert. Warmer than Bryce. There's good roads to the Island in the Sky Visitors Center at Canyonlands...Harder to get to Needles VC. About 50 mi. South of Arches is Newspaper Rock SP...100s of petroglyph's.
Colorado Nat'l Mon. is about the last of the sandstone canyons if your going East.
The Grand Canyon South Rim is in the 7000-7500ft range as is I40 Flagstaff/Williams. It's getting to be winter there...more humidity than those northern destinations. North Rim is probably closing. Keep the weather radio on and expect some delays, but the West isn't in true winter yet. You are setting yourself up for using I70 across the Continental Divide...that can be tricky Grand Junction to Denver. It is snowing up there now.
