You could plant turnips. The birds love the greens and they grow in cold weather. I just planted about $2 worth of seed and got a 20 square foot area covered with tiny little turnip sprouts. It only took about 3 days for them to sprout. This is my first time growing them but the guy at my local feed and seed store said they would make a fine winter green plant for my birds. And I can eat a mess of turnip greens myself every once in a while.
I don't have a run I could build a frame in so I just sowed them in my garden spot that I had just finished cleaning out after this past summers crop.