You say they had horses for those types of traveling, except they most likely didn’t. Only a successful farmer... We can't make a universal rule like this. Eve

You say they had horses for those types of traveling, except they most likely didn’t. Only a successful farmer... We can't make a universal rule like this. Everyone has a particular mental image of how farming worked long ago, but circumstances varied. Horses can eat a wide variety of plants, including something that is growing wild right outside your door. The density of farmers probably had more to do with whether they could afford a horse than anything else had. In locations that hadn't been farmed relentlessly for centuries, there was spare pasture for a horse or two to feed themselves. For an example, just look at traditional herders. Those people are poor as dirt even today, yet they all have horses. Or look at swiddeners. They didn't move every year, but they moved often enough that not every square meter of land had been converted to intensive agriculture. Many of them, both today (when swiddening is rare) and millennia ago (much more common!) had all sorts of livestock including horses. Many ancient farmers couldn't have owned horses because they didn't have a way to feed them. Many other ancient farmers did own horses and could feed them.