Hi,
https://www.openstreetmap.org/way/1306340709 is probably a riding arena and not a riding centre; it does not make sense to map a small riding centre inside of a larger one. Riding arenas are usually tagged leisure=pitch + sport=equestrian (in JOSM you can use the preset for sport=equestrian), like here: https://www.openstreetmap.org/way/1189183433

https://www.openstreetmap.org/way/1306340688 and https://www.openstreetmap.org/way/1306340705 don't look like riding centres either. I don't know what these areas are. If they are pastures they can be tagged landuse=meadow + meadow=pasture, see https://wiki.openstreetmap.org/wiki/Riding
Please use the tag leisure=horse_riding only once for every riding centre, see https://wiki.openstreetmap.org/wiki/Tag:leisure=horse_riding#When_not_to_use