In the ancient times no stirrups were invented yet. They did however use a saddle. Originally of celtic origin the horned saddle did serve the equites a stable horseback experience without loosing the connection with its mount. It has long been a discussion on how these saddles were constructed originally. Did they contain a wooden frame (called a saddle tree) or were it padded pieced stuffed with felt or straw?
Based on the leather remains as found in Valkenburg z.h. the late Peter Connolly did propose a first reconstruction with a wooden tree. Nowadays we have a bit more evidence as was known to Connolly. Further saddlecovers have been found in Carlisle and recently bronze saddle horn covers with the wooden horns still present in Pompeii. At least a wooden tree seems to have been known to the Romans.
Although I’m not a saddler I’ve finished the leatherwork of three Roman saddles sofar. For these the trees were made by experienced saddlers, so they don’t hurt the horse back.
The Roman cavalry saddle at the Roemermuseum in the Archeological Park Xanten (germany) 
A roman saddle with a saddle cover based on the Carlisle, united kingdom, finds