Riding without a saddle:
— A bareback rider.

synoniem: barebacked.

Roget 226: divested etc. v.; bare, naked, nude; undressed, undraped; denuded; exposed; in dishabille; bald, threadbare, ragged, callow, roofless.    in a state of nature, in nature's garb, in the buff, in native buff, in birthday suit; in puris naturalibus [Lat.]; with nothing on, stark naked, stark raving naked [Joc.]; bald as a coot, bare as the back of one's hand; out at elbows; barefoot; bareback, barebacked; leafless, napless^†, hairless.    ... meer laten zien

Without a saddle:
— She prefers to ride her horse bareback.

synoniem: barebacked.