I can tell you what not to do... When my daughter was in 4H we went a bit overboard and put her and the horse in full medieval costumes. We had been using this horse in medieval recreation so he was very used to all the weird stuff, but the judges were terrified that there was going to be a wreck. From the moment she went into the arena, there was a 'helper' within two feet of them the entire time. Due to the 'safety concerns' she only got fifth, though the crowd thought she should have gotten first.
Between the two of them, they were wearing about 150 pounds of deer hides and over $500 in armor.
I'll see if I can find some pictures, but a couple of years ago we turned a palomino into a poodle. I took and old sleazy, cut the neck off and glued on tufts of polyfill with spray adhesive. I spray painted it to match the coat color (would work with a chestnut too, poodles come in that color!) I used Elasticon to make the puffs for the legs, laid out strips long enough to go around the leg, attached polyfil and spray painted. (we stuck the elasticon to wax paper, so it wouldn't stick to anything else until we were ready to use it). We wrapped the lower leg in plain old vetwrap and then stuck the elasticon to that so we didn't have any sticky's on the horse's legs. We braided the tail, folded the braid back up on itself and attached another poof, made just like the leg ones over the end of the braid, just below the tail bone. Put a poof of polyfil on the top of a halter and voila! The horse becomes a poodle. You could dress your handler up like a dog handler, and maybe put a 'collar' and a bow around the horse's neck. We dressed all the other kids up like dogs and sent in the 'handler' holding all the leashes.