If it's hot (say, above 70 degree F), a well-trained man can out run a horse over a long distance. If it's cold, the horse will win. The horse's cooling is largely dependent its breathing which is constrained by its pace.
FEI Endurance horse run to 100 kms in over 15 hours. Ultra-marathons of 100 miles are won in just over 14hrs. In UAE, in Slovakia, in Wales. In all conditions, man beats horse over distance.
