Hay, straw, bags of leaves all would do nicely, and then could be used in the run. They would already be well on their way to composting. What I'd do would be this: place hay, or straw, or bags on the north side, as well as the side where prevailing wind tends to come from. Staple clear plastic up on the south side. One thing to be aware of when purchasing hay or straw: many fields and crops are heavily treated with herbicides. Some of the newer ones persist in the environment for a VERY, VERY long time. Even to the point that cows who eat the hay then have contaminated poop. The contamination will persist even through the composting process, and show up in a stunted garden that will take YEARS to recover. So, buyer beware. I only source hay from one farm, and even though I know this guy and buy from him every year, I ask him before I pick up every load if the fields are ever treated. I'm happy to see a bale of hay that is full of weeds! Ketterman, where you live in Amish country, this may not be an issue for you. BUT, ASK BEFORE YOU BUY.