Less tiresome, but if you set the pace hard, you can travel a greater distance for the same amount of time.
The Mongols used several horses, changing out regularly to keep them all relatively fresh, so they could keep the same high pace throughout.
I know many cultures and/or organisations use relay stations with fresh horses so that riders or messengers can change their mounts then hurry on to the next waystation.
The Pony Express had waystations set up every 10 miles as that was about as far as a horse could gallop (~30mph) before it tired.
The Romans had a similar system and there's apparently a map of their road system along with their messenger changeover points, or stationes.
I'm not familiar with horse anatomy and their biology, so will need to do some research.
Edit: D'oh, I'm an idiot. The primary reason is apparently thermoregulation - horses have less surface area to volume ratio than humans and additionally generate greater heat when exerting themselves: link.