We had a games day one time back when I was in Pony Club.
We did a keyhole race - across the ring, around a barrel and back.
A race where we had to put an envelope between our knee and saddle go up the the barrel (from the keyhole race), drop the envelope in a "mail" box. Then return to the start line.
We also did an egg and spoon race and something with water... I think we each had a full cup and rode down to a bucket on top of the barrel and poured in whatever was left (a lot was lost on the way to the barrel!). We went back and forth until the water in the bucket was to a certain line.
We were on teams of 3 or 4 and every race was a relay race. It was alot of fun :)