Hi,
https://www.openstreetmap.org/way/1312659165 looks more like a riding arena than like a riding centre. In OSM riding arenas are usually tagged leisure=pitch + sport=equestrian. The tag leisure=horse_riding is for complete riding centres, compare
https://wiki.openstreetmap.org/wiki/How_to_map_a#Riding_centre_(equestrian)
https://www.openstreetmap.org/way/1022553900 (example)