Hi,
https://www.openstreetmap.org/way/145321678 and
https://www.openstreetmap.org/way/1453216829
don't look like riding centres (leisure=horse_riding); they look like riding arenas, similar to
https://www.openstreetmap.org/way/787822093.

Are you sure that
https://www.openstreetmap.org/way/1453216786 is a building?

Example riding centre with arenas:
https://www.openstreetmap.org/way/1207911689#map=17/51.723286/-1.942221&layers=PN

In JOSM you can tag riding arenas with the preset for sport=equestrian.
