Well, the Graf Lehndorff Institute for Equine Science teamed up with the Brandenburg State Stud in Neustadt, Germany and the University of Vienna, to study the competition nerves of horse and human teams.
Heart rates of the horses and their riders were monitored during at-home practice and while doing the identical activity in front of an audience in a competitive environment.
Both horses' and riders' heart rates increased while doing the activity. The riders' heart rate increases were more marked when in competition than during practice (as were other cardiac measurements and amount of cortisol released), suggesting that human beings get nervous in competition but horses do not.
Based on these preliminary findings, it appears that horses don't feel pressure as much as people do. Could it be, competitively speaking, better if the horse was the one primarily directing the team rather than the rider?