I've had pretty good results from cleaning up the loose hay chaff in the barn, and spreading it on the thin spots in my pasture. Originally, like 15 years ago, I intended, just to mulch those areas until it recoverd in the spring, I ended up with some pretty nice Rye Grass, Blue Grass, Clover, and Alfalfa there.
The area where I ground hay with a hammermill, for an old mare I had, has the prettiest grass/clover/alfalfa, growing on 6" of #4 limestone.
Depending on how you are equipped, baling, and redistributing may be an option.