trevanian
Rear Admiral
^ Stewart's and Shatner's interaction off screen, resulted in a increase in Picard's ability to ride a horse with skill during Generations. Definite impact on the character.
Wasn't Picard already established as being a skilled horse rider throughout the show?
Melinda Snodgrass wrote a teaser 2nd season that gave this impression about Picard, and even gave an interview to the effect that Stewart was okay on horseback, but that wasn't really borne out by anything on screen.