Apparently this has been asked before btw. The short answer is that Greece has pretty rough terrain which would slow a horse down significantly and that horses aren't necessarily faster at such a loooong distance run.

u/stylepoints99

https://www.reddit.com/r/AskHistorians/comments/4pw0px/why_did_the_athenians_send_a_runner_not_a_rider/?st=j8b9tbcb&sh=090c569e

So dumb question I guess, is this where marathons (the athletic event) comes from?