Hi,
All the areas that you have tagged leisure=sports_centre + sport=horse_racing are far to small for horse racecourses. A good example for a horse racecourse is  https://www.openstreetmap.org/way/5215699.

https://www.openstreetmap.org/way/1314164175 is a riding arena (I can see than on Geoportal and Bing) and should be tagged leisure=pitch + sport=equestrian (like https://www.openstreetmap.org/way/1242430304). What the other areas are I don't know; maybe arenas too or paddocks (landuse=animal_keeping) or pastures (landuse=meadow + meadow=pasture), see https://wiki.openstreetmap.org/wiki/Riding