My chickens choose to go outside and forage when it is 4 degrees F above zero. I supect they would forage when it is even colder but I haven't had it colder when they are awake to try it.
My chickens are usually afraid of the snow when they first see it. Last winter, some got used to it and would go out and forage in it if weeds and grass was sticking up through it. I've had chickens walk through 9" of snow to check out the compost pile. Some never get used to snow and never go out in it and all are afraid of it when they first see it, but some are braver and more adventurous than others.
My chickens have no problems with snow! If we weren't having a crazy warm winter (so far, although some crap weather headed our way tonight/tomorrow) I would be jumping up and down for a 20 degree day!
No worries about the depth, they're light animals and their feet are designed almost like snowshoes. They won't sink down. We get snow (or used to, when we actually had winter. WTH, weather?) a lot up here and our girls love it. When it's all powdery and fresh we often see some of them trying to use it like a dust bath, really, really cute. Just make sure they have a warm space to go back to as they please - they're not stupid, they won't stay out in the snow to the detriment of their own health and will go back to warmth when they need it.