Hi,
all 8 areas that you have tagged as riding centers (leisure=horse_riding)
https://www.openstreetmap.org/way/1431607617
https://www.openstreetmap.org/way/1431605755
https://www.openstreetmap.org/way/1431605756
https://www.openstreetmap.org/way/1431605759
https://www.openstreetmap.org/way/1431605782
https://www.openstreetmap.org/way/1431605786
https://www.openstreetmap.org/way/1431605787
https://www.openstreetmap.org/way/1431605790
do not look like riding centers; they look like riding arenas or the round ones as round pens. They should be tagged with leisure=pitch + sport=equestrian, like https://www.openstreetmap.org/way/1429285368.
Here is an example for a riding center with some arenas:
https://www.openstreetmap.org/way/1228517621/history#map=17/47.747609/-122.140304&layers=P
Compare
https://wiki.openstreetmap.org/wiki/How_to_map_a#Riding_centre_(equestrian)