The horse was probably not a good example. Those things can take some heat and do sweat. It is more likely they were persistence hunting game.
Persistence hunting is an interesting topic. We had a discussion on here about it before when we discussed barefoot running. This is before I saw the light on that subject (I am now a minimalistic mid-foot runner). I wanted to see if it is doable in the US, hunting antelope got me thinking, and some guys tried persistence hunting them in WY and then some other guys (pro athletes) were successful in NM.
http://www.outsideonline.com/outdoor-adventure/nature/Fair-Chase.html
Not sure if they would have made it without a fence. But then, prehistoric humans were probably a lot better at gauging the situation and following an animal than the average modern runner doing an experiment.
The wikipedia site on the subject has a lot of info and further reading:
http://en.wikipedia.org/wiki/Persistence_hunting
G