I have changed it. Explanation: A feature (e.g. riding arena) can be part of another, larger feature (e.g. riding centre), but that does not make it a different feature itself, it remains what it is (e.g. a riding arena) and should be tagged accordingly. The building that was tagged with leisure=horse_riding was also not the complete riding centre, but probably only the riding hall belonging to the riding centre (which I have now mapped as a node).
Another example from your region: https://www.openstreetmap.org/way/494425529.