Horses in medieval times might not have been as common as you would think…
This might surprise you, but the most common plowing animal for medieval peasants was an oxen, not a horse. Not only did horses cost more to buy and feed, but they also could not be sold for as much when they grew to old to work. It was seen as bad to eat horse in medieval time, but people were more than fine with eating oxen, which worked out well due to them having more meat in old age. Horses might live longer and might be faster workers, but for a medieval peasant, the cost of owning one was often too high.
Do not get me wrong, there were peasants that did use horses, and eventually the horse became the most popular work animal, but not until the early modern era when animal feed lowered in price.
When a peasant did own a horse, it was likely bought at an old age so the price would be cheaper. Horses could be used for more variety, but an oxen was the most common for working in a farm.
The reason why I am bringing this up is that whenever I am reading a book and the characters need to get somewhere fast, they can magically find a healthy young horse- which is often not even a work horse- to ride. Likely, if your characters come across a small poor farming town that did have a horse, the horse they would find to buy would be past its time.