Horse Shows In The Sun. HITS, Inc. produces high-quality, international-level hunter/jumper horse shows. Based in upstate New York in the village of Saugerties, HITS has been producing shows since 1982 and is now a nationwide company with world-class circuits in California, Florida, Arizona, New York and Virginia. HITS Desert Horse Park is just minutes from La Quinta. It is located on Airport Boulevard in Thermal and this world-class event is not to be missed. Visit the website for a complete listing of show times.