Hi,
https://www.openstreetmap.org/way/1379439403 does not look like a horse riding center (tag leisure=horse_riding); it rather looks like a horse riding arena (tags leisure=pitch + sport=equestrian), like https://www.openstreetmap.org/way/1363141756; doesn't it?

https://www.openstreetmap.org/way/165849671 is an example for a horse rodong center.