Let's not talk about the Zhao state anymore. In Qin, all the cavalry combined probably don't exceed 80,000, and that includes those from the Northern Frontier. The Zhao state should have a bit more, but not by much. As the main force against the Xiongnu, the Frontier Army is also cavalry-based. There are 70,000 cavalry stationed in the Dai Territory. The ones who have come this time couldn't possibly be all of them.
Maintaining a cavalry is not easy. The resources required are much greater than for foot soldiers, especially the warhorses. In this era, without the "Three Treasures of Cavalry Warfare," a warhorse would generally have to retire after just a few years. They were nowhere near as enduring as the horses that came after the advent of these "Three Treasures."
