There are however no depictions of horse riding in art before the 1st millennium BC, or in the earliest texts of Indo-European speakers. So, some archaeologists have sought alternative ways of establishing that horses were ridden. To ride a horse, one needs a bit which is put in the horse's mouth and reins by which the horse is controlled. The teeth of a horse that have a hard bit will show evidence of wear in a distinctive pattern, and this will allow us to infer that it was ridden.
The following excerpt from a recent review of Robert Drews' Early riders: the beginning of mounted warfare in Asia and Europe by Karlene Jones-Bley in Journal of Indo-European Studies vol 33, no. 1/2 shows how this ingenuous hypothesis has not survived radiocarbon dating.
Nevertheless, the entire bit wear thesis collapsed once the skull of the "cult stallion" was subjected to radiocarbon dating and was found to have died before 700 and 200BC. Thus, even if the evidence for bit wear were valid (and there are those who still question even this), it didn't happen at Dereivka until the Iron Age when no one doubts the existence of horse riding and hard bits.
Dr. David Anthony, who proposed the bit wear hypothesis has sent me an e-mail in which he gives some additional information.
The date of the domestication of the horse is still poorly understood, but horses certainly were domesticated and used for riding in the northern Eurasian steppes by the middle of the fourth millennium BCE, and they were grouped with cattle, sheep, and humans in funeral rituals that excluded obviously wild animals during the fifth millennium BCE. The 3500BCE date for riding is supported at Khvalynsk in northern Kazakhstan, dated 3500-3000 BCE, where in addition to bit wear on horse premolars, stabling soils full of horse dung were found, and whole horse carcasses were regularly brought into the settlement for butchering as a regular practice over the course of hundreds of years. The occupants had no cattle or sheep, no draft animals other than horses, so if the horses at Botai were wild it is difficult to understand how they were brought into the settlement. The inclusion of horses in human graves dated 4500 BCE is documented at Khvalynsk on the middle Volga, a cemetery where the sacrificed animals included parts of 52 sheep/goat, 23 cattle, and 11 horses, and no obviously wild animals. Khvalynsk sites also have yielded stone maceheads shaped like horseheads and bone plaques carved in the shape of horses. The bit-worn horse teeth at Dereivka were re-dated to 700-200 BCE by me, the same person who identified the bit wear, but the article in which I announced the re-dating of the Dereivka teeth also described the evidence from Botai and Khvalynsk. Dereivka was not the only site with early bit wear in the steppes. No credible or accurate criticisms of bit wear analysis have yet been published, so the detection of bit wear remains a valid way to identify bitted horses in the archaeological record. Please see Anthony, David W. and Dorcas Brown, 2000, "Eneolithic horse exploitation in the Eurasian steppes: diet, ritual and riding," Antiquity 74: 75-86.