[Rollos]

It wouldn't have affect humanity that much. Farmers still could have used oxen to plow fields, which is the main purpose horses were used for. Contact with China and other countries might have taken a little longer, and trade might have been slowed down, but not by much, maybe 100-200 years.

As for military, they didn't matter much in the conquering of the Americas since most peoples died by diesease. As far as Eurasia, I still think everything would be the same since no one civilization's military had a monopoly on horses for a significant period of time.

In short, no, the absence of horses would not have a great effect on human progress.