I got to watch that this spring, when our mare flagged the cat then pitched it. Cat no longer hangs right under the horses' feet. And all horses that aren't either quite old or arthritic play like this. Ours spend their time killing an old soccer ball, a ratty-ass horse blanket and a couple of traffic cones.
I know a horse who likes to pick up really big sticks and chase the other horses around the pasture with them. It's like he's threatening to whip them. He can do it for hours unless a human stops him from harassing his friends. It's so entertaining.