Horses may have been ridden in battle as early as the Bronze Age (Chechushkov et al. 2018)

Over at the Journal of Archaeological Science at this LINK. Below is the abstract. Emphasis is mine:

The morphological similarities/dissimilarities between antler and bone-made cheekpieces have been employed in several studies to construct a relative chronology for Bronze Age Eurasia. Believed to constitute a part of the horse bit, the cheekpieces appear in ritual contexts everywhere from the