In the long run, if at all possible, I'd move the coop and run to higher ground. As an interim fix I'd get a couple bales of straw and lay it out thickly across all the muddy parts. In Washington, where I am, my run gets pretty wet in the winter. I go through a lot of straw, and although I still sink in the chickens do not. For a similar reason we are moving one of our coops to higher ground this summer, so you're not the only one who didn't think about that ahead of time. LOL