This question arises from the news report “NY Marathon Winner Tests Positive For Performance-Enhancing Horse” from that esteemed paper The Onion. Could a horse actually win a marathon with world-class runners?
I don’t know what caliber of runners participate in the annual Man vs. Horse Marathon in Wales, but the horse usually wins. A description of the course, along with a bit of the history of the event, is given on the official website.
Looking at that article in detail, the best horse times are about 1 1/2 hours for 22 miles (perversely, the race isn’t an actual marathon). That may or may not include a 15 minute delayed start for the horse, the article isn’t clear. The marathon world record is 2:03:59 (Haile Gebrselassie, 2008) for 26 1/4 miles.
Not completely conclusive, but I’d say a man couldn’t beat a horse over a marathon distance. However, humans are built for endurance running. It’s quite possible a man could beat a horse over a longer distance, especially as we can eat and drink while on the move. This is the basis for persistence hunting.
I’m not sure how long the race would have to be for the human to have an advantage.
Comparing two races of 160km both held in the Siera Nevada mountains of California.
The Western States Endurance Run has a record finish of 15 hours 36 minutes while the Tevis Cup the average finish time for a horse is 10 hours and 46 minutes.
I think it will take a while for any single human to out perform a horse on endurance. I may be mistaken but wasn’t persistance hunting groups of men working together?
Without a rider urging the horse on the man would beat it everytime it found some decent grass to eat. 
Really, the horse has no incentive to run that far unless it was being chased by a preditor (say a pack of wolves) and even then would most likely be caught and killed or escape and rest before it finsihed anything near a marathon run.
IIRC, Western States started as a horse race, but the first human competitor won and it changed into a people race. No, I don’t have a site, my memory is from a SI article while I was in college - the early 80’s.
In general, the sunnier, hotter and drier the conditions, the shorter the distance for a human to outrun a horse.
Lots of interesting discussion on this topic in
Oops, talk about repeating history…
A few points. During the English Civil War a Royalist soldier was captured and offered his life if he could beat a horse in a race. Don’t know the distance, but it wasn’t more than about a mile. He won, too. They still killed him, though. The Welsh race was run by a man a few years back too. And persistence hunting, effective though it is with antelope and the like, has never been relied on against an animal like the horse, an animal bred for endurance for several millenia by man. Man is good at endurance running, better at selective breeding.