Enough time has passed that the 1st episode from season 4 of Strange New Worlds is now open for memery goodness. Episode 2 “The Griffin Incident” on the 30th, just in time for Hallow Hemmer-ween!
TNG s6e16 “Starship Mine” aka “Star Trek Does a Die Hard” and SNW s4e1 “Valles Marineris”
Edit: Season 6 of TNG, not 7
I’d bet dollars to donuts you could trace horseback riding recurring throughout the series to DeForest Kelley. DeForest was a well established actor in the Western genre before his role in Star Trek. And at a certain point he was getting screwed on the royalties of the Star Trek films, so William and Leonard pushed to get him a producer credit on the next film. That film also had a camping in wilderness tribute to DeForest at the beginning. I think the first horse scenes were Kirk and then Kirk and Picard.
While I don’t doubt Kelly’s influence further down the line, credits to navy beans horses were a passion of Gene’s from the get go.
Not to mention, Bones wasn’t in “The Cage.”
I know shamefully little about Gene, so that makes sense too if he was a horse guy.