Stuff a (new!) athletic sock with straw, fiberfill or cloths, leaving about 4" unstuffed at the bottom. The toe of the sock forms the horse's muzzle. I chain stitched a mouth in red yarn and glued black felt patches where the eyes should be. Stick a 3' (you can cut it to match the height of your rider) 1" dowel into the sock to about 3" from the top of the sock (this leaves a little padding to keep the top of the stick from hurting anyone) and tie off the bottom of the sock tightly.
The kids could then personalize their horses, adding manes and forelocks, halters, reins, eyes, barding- whatever they could think of. Then later, we had horseback races. The horses cost about $3 each to complete, so its not a big deal to let the kids take them home after the event. I've kept a couple of generic ones to take to events in the children's activities box to use during the "exhaust the kids prior to snack and story telling" period.
Generica