Some chickens are very finicky about walking on even the slightest bit of snow -- one thing you can do is toss a thin layer of straw or hay over the snow in at least part of the run. Last year my flock was one of those finicky bunches, they would line up at the pop door and watch me come out with a bale after a fresh snow...then leap frog from spot to spot as I got it scattered like a bunch of kids playing "don't touch the lava".