Equine influenza would be the likely plague in question. However, as I recall, we're talking about mortality rates no worse than say, the Black Death - with a much faster recovery rate; mares can start breeding at age 4, and have between 12-16 foals in their reproductive lifetime.
Now if you want to play with a more extreme version of the disease, with your starting point: we are still just talking about a few centuries of delayed movement. And on foot? Nope, they had very recently managed without horses and would continue to do so.