Could be a viable solution.^^^^Put a picnic table in there and tack a piece of ply-wood against the windy side to form a lean-to wall. Not only will it give them a protected area to hide under when it snows, but you'll essentially double your "floor space," since they'll have a second story!
@tweetzone86 can you post pics of your run?
Might help garner some more ideas.
I have to shovel part of my run, we get feet of snow in our lake effect region, and keep the snow knocked off the mesh roof. Luckily there is one small area of run under the coop with wind blocks for shelter...and the coop is pretty big for the days no one will go out.