Walk. Seriously, people walk in general, not ride horses. You use the horse to carry cargo, or haul a wagon (oxen would be better for pulling a wagon - they eat less so despite being slower they are more economical, plus the anatomy of oxen make a harness easier). The people though don't ride in the wagon they walk behind. Wagons without modern suspension are rough rides and you can walk farther than the horse or oxen can in a day, and just as fast. Thus horses were only rarely used for human transport through most of history.
The only time horse transport makes sense is when you have a regular system of change points and so the horses "run" (probably at a trot not a run, but I'm not an expert on horses so if details matters do your own research) faster than you can for an hour or two then you trade horses while the first horses rest until tomorrow. In this way you can travel a lot faster than you could by walking, but it depends on the whole system which is very expensive to setup/run. Anyone who needed to save money would walk even when that system existed. Thus such systems - where they even existed - were often used for mail where spread across thousands of letters the cost was cheap enough that you could afford the speed.