Yup, the stirrup. Part of your saddle. Has anyone actually considered writing in a period before it was invented? Or, if you've got a world you're working on a timeline for, when was the stirrup invented, and how did that change warfare for your people?

Before the stirrup, you couldn't brace yourself in the saddle. This affects the way cavalry fight. This probably has big effects that I'm completely unaware of. So! Anyone have any thoughts on how the lack of the stirrup changes war?

The stirrup allowed the rider to crash into infantry, allowing for cavalry charges.

The Indians didn't always use saddles, but they were awesome riders and no less dangerous in a fight. I think it was because they chose a way of fighting that used their advantages (extreme mobility) instead of disadvantages (instability on the horse because of a lack of stirrups).

They also fought at a time when old fashioned cavalry charges were limited in usefulness, and their whole style of fighting never would have used it anyway. But you could certainly base a stirrup-less group's mounted fighting style off of what the Indians did.