First of all we can't equate Shadowfax's run to that of to a cyclist since the cyclist runs a course on a paved surface, which Shadowfax didn't have the benefit of.

Instead, let's equate Shadowfax's run to that of something like the Tevis Cup, which is a 100 mile race course that must be comleted within 24 hours, and the horse and rider both must be physically well (as determined by race vets and doctors) by the end of the race. Further, the Tevis Cup is over rocky and mountainous territory, but there is a trail, so I think that will still equate out for Shadowfax's run.

Now, the best time for the completion of the Tevis cup is about 14 hours. There are numerous stops and checks for physical wellness, none of which Shadowfax had the benefit of (only about half of Tevis competitors actually complete the race) and the horse does not run the entire time (no horse could). Finally, Shadowfax had to cover about time and a third each day for three days in comparison with a Tevis horse.

Either way, we are talking about an average speed of 7 mph for 14 hours for the fastest Tevis Cup winner. Shadowfax had to go faster then that for THREE days running, roughly 10mph (assuming 134 miles per day with a 14 hour run). At the end of those three days IIRC Shadowfax is still fresh and able to go. That's not a bad trick for horse. In comparison with our modern equipment (aluminum or alloy horseshoes, plastic tac, etc) almost any contemporary horse would be killed having to go that distance in that amount of time.

-RR