The National Horse Show is the oldest continually held horse show in the United States. It was founded in 1883 in New York and held there until 2002, when it moved to Florida and then to Kentucky. The National Horse Show offers competition for hunters, equitation, and show jumpers.The National Horse Show is the oldest continually held horse show in the United States. It was founded in 1883 in New York and held there until 2002, when it moved to Florida and then to Kentucky. The National Horse Show offers competition for hunters, equitation, and show jumpers.