Here are some of the things that I do with my summer camp:
I make a binder that goes over colors, tack, grooming, safety, measuring, etc. We get little fun stickers cheap at wal-mart and they love decorating their binders and taking them home with them. I include word searches and cross words in the binder.
Put double sided tape on index cards and label the parts of the horse. Let the kids stick the cards to 'ole care less kinda horse.
Horse Jeopardy - BIG HIT - make a jeopardy board on a piece of poster board. Some of my topics include breeds, tack, colors, behavior, grooming, etc. I usually stick post it notes over the categories that have been guessed and come up with the questions as we go along. Put them in teams, they have a lot of fun with it.
Horse beauty contest - if you have the room to bathe several horses at once, let them have a little fun with it, braid them, glitter, etc, judge them at the end. They also tend to wash themselves as much as the horses so its good for a hot day.
Horse Costume contest - I usually do this on the last day of camp, must have very understanding horses. I had a pony dressed up as a paper indian one year and my mini gelding was a fairy with a purple tutu (sp?) ironically weeks after being gelded.....
Horse games - toilet paper race, egg and spoon race, relay race, water race. Put kids in teams and give each team a barrel, some games are timed, some games are races. Put speed limits on it as needed. I usually say trot only, more than 2 strides of canter is disqualified.
Simon says is a great, controllable mounted game. Around the world and Indian Dismount are a bit more challenging. Ride-a-buck is always a good one as well. Have each kid bring a dollar with them, winner gets all the dollars. If they don't want to use money, you can do it with a piece of paper.
The boot race is a fun game that doesn't involve horses. Have all the kids put one boot in the center of the arena, have kids by the rail and give a go signal, the first one to run in, get their boot and make it back to the rail wins. You do need quite a few kids to make this game fun though.
Body paints for horses is fun if you want to.
Invest in a slip and slide or small kid pool. Water baloons are fun if you don't mind the clean up.
Horse shoe picture frames are a fun craft, you can also pick up small ceramic horses in craft stores really cheap for painting.
I had a couple of teenagers with nothing to do one summer, so I gave them a camera and said have fun. The kids parents loved getting a CD of what they did at camp.
We also have had a lot of fun with line dancing lessons if you know someone that knows some easy dances.
"The Blind Horse Game" - sounds terrible, but a lot of fun. No horses involved. Blindfold one kid and have them put a headstall over their head and the bit in their hands. Have the other kid stand behind them with reins and set up a small obstacle course. This has worked wonders to help kids be more aware of the signals that they are sending and put a lot more thought into communication with the horse (and each other).
Of course, give rules to these games according to the level of your kids. I have often found that if "barn chores" are part of your daily routine, then taking one away can be a great reward. I usually do games on Fridays, the winning team still has to do all chores besides one of their choice (stalls, buckets, raking, etc.)
Hope this helps, have fun with camp!