Kirk and Picard on horseback
Horseback riding was an ancient Earth activity in which an individual rode on the back of a horse.
Christopher Pike was an avid horseback rider. He owned several horses. (TOS: "The Cage"; SNW: "Strange New Worlds", "A Quality of Mercy")
Jean-Luc Picard was a serious equestrian rider. He even owned his own saddle. (TNG: "Starship Mine")
James T. Kirk was also an avid rider. When Captains Kirk and Picard were both trapped in the Nexus, they had the opportunity to ride together. Kirk realized that the Nexus was a false reality when, on horseback, he had no trouble jumping over a ravine that previously, in the real world, was a difficult challenge. It was only after this realization that Kirk decided to assist Picard to escape the Nexus and to stop Dr. Tolian Soran on the planet Veridian III. (Star Trek Generations)
According to her biography in Star Trek: Starship Creator, Sarita Carson lists equestrianism among her interests.