my wife rides in a horse event called endurance. She rides Arabian horses which are built like marathoners Typical ride is 50 miles per day. She's done a 100. I pit crew for her. Over pretty rough terrain (up and down 3000-4000ft) she averages 12 to 15 mph. A conditioned horse will smoke any bike rider (including Lance) going uphill, they just keep going and going at a fast trot. Downhill you got to slow down unless it's sorta smooth and a low grade (less than 5?) or you will wreck their legs. They will jump low obstacles easily, but will spook at a gum wrapper and you'll have a rodeo.