I can't find a quick source to back this up, though.
But also bears and no doubt many more.
Even within ancient to medieval cavalry this tradeoff existed; the horse one rode to the battle would often not be the same breed as the horse one rode in the battle.
(cavalry having arisen in the first place because a slow horse is still much faster than a fast man. infantry that can't run can't regroup)
This might be true, but the citation says the opposite:
> In 2013, extensive forestry works meant the organizers had to modify the route considerably, resulting in a course of nearly 24 miles, instead of the usual route of just under 21 miles. Despite a very hot day, the longer and hillier course favoured the horses, with 2011 winner Beti Gordon comfortably beating the first man, Hugh Aggleton.
> Following a number of criticisms of the extended course in 2013 and 2014, the course for 2015 was shortened back towards 21 miles. This provided a more even match between man and equine
Consider that cavalry wipes the floor with infantry in terms of how much ground can be covered in a day. Don't think soldiers are selected for speed? Consider also that we have an inscription from an Egyptian pharaoh commemorating the excellence of his soldiers, as measured by the speed of their march.
Taking world record 5k (5000m/12.58min) ~= 400 m/min
versus a top CCI run (6398m/9.97min) ~= 640 m/min
we see that at these shorter distances the horse has a distinct advantage.