[JPKab]

Horses absolutely do sweat.... however, this is where the bipedal aspect comes into play.

Not only is a bipedal gait more efficient over long distances, but the fact that humans have a mostly hairless torso which is directly perpendicular to the direction they are running means two things: a maximum amount of surface area of sweaty skin is being exposed to moving air vs. body mass it has to cool. Much greater than a quadraped's.