A carriage or buggy was a type of land vehicle that was in use on Earth, especially prior to the invention of the automobile. They were generally pulled by horses. Carriages used for cavalries, especially in the Roman Empire, were generally chariots.
In an alternate timeline in the year 2263, due to the fact that the USS Franklin was a much older starship than was the recently-destroyed USS Enterprise, Sulu found it quite primitive, and he compared it to a horse and buggy. (Star Trek Beyond)
In 2374, on the holodeck of the USS Voyager, Kathryn Janeway walked with a holographic recreation of Leonardo da Vinci to his carriage when he was about to take a trip to France. (VOY: "Concerning Flight")