I've been watching this thread to see if any locals would add comment and am hesitant as a far east southerner……… but we do go out to Bluff Utah several times a year including the winter and maybe the perspective of a fellow "East Coaster" might be helpful.
In my experience in the greater 4 corners so many things are stratified by elevation. 5000 to 6500 = JP (juniper pinyon) 7000 to @ 8000 is Ponderosa. Etc. Same is true for snow. If you're high enough for Ponderosa you're high enough to likely have snow on the ground…maybe a lot of snow on the ground, anytime in winter and that might be why this is the elevation at which the Ponderosa's appear. Your marginal elevations are going to be 4500 to 5500 where it will snow but hopefully the snow won't last or be a big problem. Below 4500 ( and maybe higher as you get further south….. unless you're along a stream bed the vegetation is getting scarce and is like rabbit bush, great sage and like kind brush. When you look at the likely places to hike you want to try to keep the elevations below 6000 and better yet @ 5500.
You also have to consider getting to the places you plan to visit. You can't get to much of anywhere without crossing some pass at 8000 plus which can be trouble in a snow storm.
We tend to divide up our trips to the broad categories of east of the river and west of the river. THE RIVER is the Colorado. For flying in we've found Vegas is easily the best for west of the river except maybe for Hanksville/Torrey ( Capitol Reef) where the east side choice (Albuquerque) is best. We've tried Phoenix and don't like it. Long Drive to everywhere except the south rim and not a great place to get a motel for the night before leaving…… which we've found to be almost a necessity given the driving and the need to get an early flight to arrive home at any reasonable hour given the time difference and etc.
We've come to greatly prefer the east side and love the town of Bluff, UT as a "headquarters" ; to the point where my brother and a neighbor have property there and a nice Airstream.
I've backpacked in the Needles in winter and while snow can be an issue especially for getting there, it wasn't a problem while hiking. Same basically true for Grand Gulch. Also Comb Ridge is an amazing place to hike as can be learned from Books by Robert McPherson and David Roberts. You could also go down around Page and hike the wave area and with some good winter warmth diving boots do Buckskin Gulch. You might also consider the Muley Twist area and the many side canyons of the Escalante; but getting to Escalante and especially going over Boulder Mt. to Torrey will be dependent on the weather, and may be more easily done on the Burr Trail….. which is another reason the whole region might be better approached from the east. Any hiking/camping over 7000 or 7200 is likely to be in the snow and 8000 and up could well be snowshoes and snow caves.
The North Rim is closed in winter for these reasons though I have been out to that rim in February by luck…… and it's really pretty in the snow. The Rim Top at Zion ( and most of the backpacking there is up on top) is also in the Ponderosa zone and might very likely be in snow. Plus you have to consider the fraught potential of a slip in the wrong place; you could grab some big air!
I haven't explored Arizona "Below the Rim" and want to check out the Sky Islands in the SE like the Chiricahua but I imagine the issues will be the same with the snow line. Also BTW the dirt roads out there can really really ugly after a snowfall and melt.
Good Luck and happy to try and answer questions