Hi,
https://www.openstreetmap.org/way/1410544002 looks like a horse riding arena and not like a horse riding centre; correct? So it should be tagged like https://www.openstreetmap.org/way/1344789415 (leisure=pitch + sport=equestrian). If this arena belongs to a horse riding centre, this centre can be mapped as a separate object (node or area) with leisure=horse_riding, example: https://www.openstreetmap.org/node/9410229893#map=19/55.927805/23.341464&layers=P