Tagging equestrian/riding centres

What is the most appropriate tags for (a) out door menage areas (i.e. out door surface for schooling horses) (b) indoor riding school building

I have used farm-auxillary for the buildings, and tagged the outdoor areas as agricultural useage, but this seems inappropriate some how.

Regards

The Germans have a nice wiki page on all the horse related features: http://wiki.openstreetmap.org/wiki/DE:Reiten
For the field the page recommends : leisure=pitch + sport=equestrian
For the riding school buildings, you can choose from building=riding_school and (amenity=stables+) leisure=horse_riding

This site may also be of help.