Hi,
All the areas that you have mapped today as riding centres (leisure=horse_riding, 9 so far) are no riding centres but just riding arenas. In OSM riding arenas are usually tagged leisure=pitch + sport=equestrian. See
https://wiki.openstreetmap.org/wiki/Tag:leisure%3Dhorse_riding
https://wiki.openstreetmap.org/wiki/How_to_map_a#Riding_centre_(equestrian)
I only recently drew your attention to this in https://www.openstreetmap.org/changeset/146932062 . Why do you still misuse the horse_riding tag for riding arenas? Is there something wrong with the Italian translation in iD? Or what is the problem?