Abandoned coop and stalls – Just toss old bedding on the compost pile?

We recently bought an old hobby farm in southwest Wisconsin. The barn has been empty for a year or two, but the previous owners informed us that over the years they’d kept chickens, ducks, goats, pigs, a couple horses, and a donkey. There is an existing (open) compost pile at one end of the paddock. Can we just toss everything (minus the trash) we sweep up from the barn floor onto the compost pile?

old stall

chicken/duck enclosures