Hi
https://www.openstreetmap.org/way/1454437728 and,
https://www.openstreetmap.org/way/1454437729 are no riding centers. The large one is a riding arena and should be tagged with leisure=pitch + sport=equestrian instead of leisure=horse_riding.
The small one (pound pen or lunging circle) is usually also tagged this way. Example:
https://www.openstreetmap.org/way/1063434544#map=19/38.221983/-77.758979&layers=P
Photo:
https://clearwindfarm.com/wp-content/uploads/2022/01/DJI_0022-1030x773.jpg
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