Unless it's really cold in the teens and the windchill is bad I open my runs in the winter...some of them love being out in the snow and a few stay in the henhouse...just like any farm animal....
when my family was growing up, they let their chickens do as they pleased in the snow. i don't remember my mom or g'ma talking about any problems. i am new to it myself but mine will walk around if they want and keep in the shelter if they want.
Mine usually fly over snow, jump and run, and stand where there isn't snow. It's so funny to see tracks that make a loop out into the snow and back into the run. Or the few foot prints and landing spots about 20 feet away.