my 6 y/o paint gelding (who acts like a yearling!) loves the big ball! I think he is the only one in his pen that plays with it tho, I havent ever seen anyone else playing with it. He is very playful and me and him play games and have fun with each other so I really think it all depends on if your horse is curious enough to push it around and see what it is.
But here are some other ideas me and my friends have tried: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.
My horses enjoy simple toys for a while, but their interest does fade fairly quickly. A clean, empty feed bag can provide a long period of fun, they smell yummy so the horses love to touch and paw and pick them up and haul them around. Just make certain they can't ingest any of the bag, it needs to be one solid, safe piece. They also like burlap bags for the same reason.
I have used the milk carton trick, except I put alfalfa cubes in mine. You can leave it loose in their pen, or tie someplace at safe height with bailer twine(Something that will break if a horse gets caught in it in any way)
My horses favorite activity when they're bored is playing king of the castle. I have a paddock with a manure pile in it and everyone loves clambering to the top of the pile and wrestling with the others. Colts especially think they're terrific, but even my grown horses love a mound. You would be surprised at how steep a hill they will climb if it's their idea.
Eating is my horse's favorite all time activity, and nothing else in the way of toys can come close. Grazing in the pasture is ideal, in the winter with hay they get bored and chew fence. One thing that can prevent that is to take 3 rope hay nets, fill one with hay and pack it tight and then put the other two nets over the first. Then hang the nets someplace totally safe. Your horse will take forever pulling one strand of hay at a time out of the triple thick haynets, and this can really occupy time. The hard part is making sure they're tied where a horse can't get a foot over them, even as they slowly empty.
I have never tried a lik-it, I don't know if my horses would enjoy or not. If I had to buy one specific toy I'd try a Snack-a-ball, the plastic balls that you put treats in and then they roll to get the treats out. To me that sounds more like something my horses would enjoy.
Good luck with your ideas