Hi,
https://www.openstreetmap.org/way/1290125703 is not a horse riding centre (tag leisure=horse_riding), it is a horse riding arena like https://www.openstreetmap.org/way/205099762. In OSM these arenas are usually tagged leisure=pitch + sport=equestrian and iD has a different preset for them which sets these tags. Compare https://wiki.openstreetmap.org/wiki/Tag:leisure=horse_riding