Whether two words or one, groundwork is working with a horse without riding or driving it. Anything we do to handle a horse is considered to be groundwork - grooming, leading in hand, etc. A rider might also talk about "on the ground." For example, "One of the worst accidents I had was on the ground." (Which is true of somebody I know - horses can still be kind of dangerous at times).
A mare being ground driven, also a subset of groundwork.