Winter in the desert is amazing...
We're going into The Maze in Canyonlands for turkey day this year. Last year we were on Cat for Thanksgiving and definitely got snowed on.
I've done mid-winter backpacks in the desert before, and it's great wherever you go, you just need to be ok with getting snowed on. The biggest threat, is that snow will be covering your access in and out of canyons, and that you might have to delay your exit, or find another way out. I was in Fish Canyon on Cedar Mesa on New Year's day a few years ago, and we were climbing out the south side of the canyon, and it was covered in snow. it was interesting to say the least, but we made it slowly and carefully. We were carrying juniper boughs to sweep away snow in front of us on sloping slickrock. But down in the bottom of the canyon it was dry and pleasant.