Saddles in general were being streamlined for comfort and the ability to 'stay in the saddle' for longer times from its advent, but the saddle in a 'recognizable' form can probably be traced to the first high-arched saddle from the Roman period onwards.

/u/Tiako goes into some measure of depth in this thread. We discuss the advent of stirrups and a more streamlined saddle originating from the Roman period.

I understand the military-focus of the question and its responses; but such a generic answer is the best I can give you with my knowledge. The long and short, from the 'high back' saddle onwards, saddles became more and more streamlined for long rides in the saddle.