Egg and spoon
Apple bobbing - Place a bucket with a few apples and water at the end of the arena have the rider ride down, dismount, bob for apples, get one in their mouth, get back on the horse and go back timed. Only counts if you keep the apple in your mouth!
TP race - Two riders ride along side one another holding a piece of Toliet paper and go at a walk, trot, canter, upon someones command until it breaks the last pair standing wins.
Dollar bill race - We always do it bare back but stick a dollar under the leg of a rider and have them walk, trot, canter until it falls out last person with the dollar still under leg wins.
I can't think of anymore.... Ugh my memory is getting bad but makes me want to do all these things again I miss this fun stuff....