A school or riding school
Corral
A padock or a arena. I Could easily be wrong.
A rosette is what we call the ribbons you win while horseback riding.
Hippodrome
A jockey.
Realy all you would call riding a horse for fun is just horse riding because you are not having a lesson if you are riding a horse for fun other wise that would be called horse riding lesson. I have been horse riding for a while know and it is very fun and all i call it is horse riding. I hope this has answered your question!
It depends on the place, Give them a call and ask.
breeches Also Jodhupers
Whatever the terrain, open ground or in the woods, anyone capable of riding a horse is a horse rider.
A hack is what most call a short ride. Can be a trail ride or they may never leave an arena.
A dapple gray.
dressage
a shed, or paddock