Make a compost pile for the spring with it. I wouldn't use it with other animals just because it's not clean.I know hay gets moldy..but I clean my duck pen daily...can you use the hay waste somewhere else? I mean..even to fluff up the horse bedding for a day?
I use pine shavings only with my ducks and chickens because it keeps the moisture out. I don't put any water or food in the coop either that keeps it nice and clean.