I'm tired and sore from riding horses all day. Hi, how are you?
Oh yes, I see you are already conversant with Equestrianism.  It relates  to the skill of riding, driving, steeplechasing or vaulting with horses.
Yes it can be all of that and more. My friend and I train them for shows and we ride them a lot too.
Yes, if we delve deeper  we can describe it as  the use of horses for sports especially the competitive ones,  practical working purposes, transportation etc