Most don't like a lot of snow, but will deal with an inch or so, especially if there are bare spots, or you shovel or walk down paths for them. It does vary by individual chicken and breed though. Some of mine think that one snow flake makes it impossible to go outside, I think my one blue cochin didn't step foot outside between October and March last year. Other ones, the bigger breeds and Wyandottes, EEs and Ameraucana especially, don't have a problem with a couple of inches of snow and will march around complaining there is nothing much to eat whole time.
