What kind of hay do you feed your horses? Maybe a little hay in there. I used feed bags for the bottom of my box for baby chickies. It was the not paper kind, the kind like plastic sort of, and then I could hose it off every day too.
wood chips may be ok if they are small chips. Maybe you can get them to sell you a bag of hay that they sweep up. Or paper towels, or grass clippings, or anything soft. I don't know if newpaper is harmful to chickens, but maybe, I had a rat die once when my mom lined the cage with newspaper and it ate it.
I put down newspaper, then a couple layers of paper towel to help soak up and diffuse little spills, then cover it with about an inch of bermuda hay so they can have traction, and the droppings don't cake up. They dry out quickly because they are not caked up on cardboard. When you want to change it all, it is easy, just roll the newspaper up and toss it.