First, you really need to be more optimistic.
The only horses I've used were from awhile back, but they were as fast as a normal hasted human. So a hasted barbarian, or monk would actually have been faster on foot than on horseback.
For me, the LACK of horses has always been a thing that ruined my immersion with persistant worlds like this. My PC's in PnP always had horses, because only a poor fool would walk for miles on end when a horse could increase your travel distance by exponential numbers and allow you to get there without being winded or sore.
No horses ruins part of what it is to be a noble, a knight, and other archetypes that some folks may want to portray. Wirth would most definitely not walk to von Zeklos Keep if he had a horse to ride, but not having them available means he's doing actions contrary to what his basic character concept entails.