One of the major weak points of The Horse the Wheel and Language is that there isn’t good evidence for horsemanship during the period of Yamnaya expansion. More recently, the genetic evidence seems pretty clear that modern horses descend from Sintashta populations after 2000 BC. Nevertheless, it’s pretty weird how fast the pastoralist Yamnaya moved. I suspect that a more primitive form of horse utilization was the norm for the Yamnaya. They didn’t have cavalry, but they may have ridden ponies to get to a location or escape the scene of a raid.
A new paper looking at human skeletons does indicate such horse-riding, First bioanthropological evidence for Yamnaya horsemanship:
The origins of horseback riding remain elusive. Scientific studies show that horses were kept for their milk ~3500 to 3000 BCE, widely accepted as indicating domestication. However, this does not confirm them to be ridden. Equipment used by early riders is rarely preserved, and the reliability of equine dental and mandibular pathologies remains contested. However, horsemanship has two interacting components: the horse as mount and the human as rider. Alterations associated with riding in human skeletons therefore possibly provide the best source of information. Here, we report five Yamnaya individuals well-dated to 3021 to 2501 calibrated BCE from kurgans in Romania, Bulgaria, and Hungary, displaying changes in bone morphology and distinct pathologies associated with horseback riding. These are the oldest humans identified as riders so far.