Update: the chickens are getting used to the snow faster than I thought they would. On the day it snowed, we got 7 inches of accumulation, and while the area I set up for them was dry and sheltered, they still had to cross through snow to get to the coop. I was worried they may not want to go in at bedtime - it was getting dark and they were standing at the edge of the snow looking displeased, refusing to step in it. So I went in the run and carried two of them across and put them in the pop door. By the time I went to grab a third, all the remaining chickens said "no thanks, we got it!" and went in all on their own!

The following morning, the snow was still there, so I watched through my chicken cam to see what they'd do when the auto door opened. They took turns standing in the doorway looking out and weighing their options, then going right back in

After a few rounds cycling in and out like that, they decided to go out. Went straight for the sheltered side and hung out there all day. By then it had dried up enough that they could dust-bathe happily in a sunny spot. In the evening they all went in no problem. The snow is gone now, but they still take a moment to stand in the doorway and take a really good look around before coming out in the morning! That's new - they used to always rush and fly out right away. I'm pleased though - they seem to be adapting to winter better than I expected. I thought the day after the snowstorm they wouldn't come out at all, given that it was in the 20s and still lots of snow on the ground, but they did.