I agree that straw or sand for the mud would probably be the best way to deal with the mud, I use straw for one of my runs. It's at the bottom of the hill, connected to another run, so it catches all of the run off when it rains and gets pretty yucky without the straw.
For green stuff, you might consider fodder boxes. I plan on building a few for my Silkies this spring since they don't get to range on the yard very often. All you do is make a wood square without a top or bottom. Put some grass seed inside (or whatever else you want them to nibble on) and cover the top with hardware cloth or chicken wire. The greens grow up through the wire cover, the birds can pick at them, but they can't scratch up the roots and destroy the plants. I also sprout lentils for a green treat for my birds. Put the seeds inside a mason jar with a cheese cloth top. Rinse them everyday and drain them well until they've sprouted, then they're ready to feed (they're also delicious on salads and in stir fry!!!!).
Good luck!
