I've used this idea for horses that like to chew. Start by folding two pieces of bailing twine in half. Braid all four pieces together, leaving a good eight inches or so open at the bottom. You can either add more twine and create a ball, or you can firmly tie a small stuffed animal (minus eyes and all other plastic parts) to the bottom. You can also use a toy with a squeaker, though be careful they don't get the squeaker out. Hang this from the top of the stall. This can amuse the horses for hours.
You can also do the standard rocks in a well-washed milk jug, minus the cap.
I gave pieces of old carpeting--large pieces--4 foot square at least-- to a young colt who had to be isolated from the herd. He had the best time, tossing them around, tearing them up. Take them away before they get too stringy.
If you do give the horse a bucket, take the bail (handle) off so he can't get a leg caught. Don't give him flimsy hard buckets that might shatter--those black rubber pans are good toys. My colts drag those all over the pasture.
Milk jugs-- put small amounts of sweet feed or oats in them, leave the top off, let the horse figure out throwing the jug around gets her a reward of a little feed.
Horses seem to like to make noise. If you can stand it yourself--a big cow bell hung in the stall seems to entertain some horses endlessly.
I've never used them, but I see those PonyPops advertised on RFD-TV.
My horse seems to love taking my grooming kit apart and flinging everything in all directions. Once he has emptied the entire kit, he takes the bucket and throws it across his pen, usually into a mud puddle. That's his favorite game.