Yes, I ride horses. Unfortunately, the riding centres are not visible on many OSM maps because the tag has been used incorrectly too often (https://github.com/gravitystorm/openstreetmap-carto/pull/3660). That's why I occasionally complain when someone uses the tag incorrectly.
There are various tagging options for paddocks. In Germany, we have more smaller and grassless paddocks, for which  meadow=paddock does not seem suitable, which is why (a long time ago) someone invented landuse=animal_keeping. See also https://wiki.openstreetmap.org/wiki/Riding