A person going long distance and a horse are NOT the same.
A person makes a lot of decisions on their own. When to walk,
when to wait, drinking all the time, eating on the run, etc.
A horse is carry weight and has a pilot with very few
instruments. And the pilot very often can't see because of the clouds.
Those are all reasons to have vet checks. They are not reasons to have
the horse held for longer than the time necessary to complete the
vetting process at those vet checks.