Not sure what its real name is but u take about 3-5 squares of toilet paper in a row and hold it between u too. The point is to see what u can do before it breaks. U could also do gymkhana games like pole bending. U could have a trail challenge or do an egg and spoon or relay races.
Some suggestions of fun games that you can play with horses include speed weavers, potato race and stepping stones. Speed weavers involve weaving in between five poles that have been set apart at an equal distance. Find more suggestions from the following site http://www.mounted-games.org/games/games.htm.
We play redneck polo. Plastic handle brooms and a playball. Soccer, get a large exercise ball Jousting with pool noodles Ring spearing Carrot trail ( set up a trail pattern and get your horse to do it in hand by following a carrot