No, historically carriages have held the right of way, and the higher their occupants social status the more right of way they had.

Well technically it's priority not right of way. My guess is that the concept was only codified with the introduction of traffic laws, which in most places didn't happen before the 20th century. Until then, "priority" in land probably came down to common sense: size, conventions, and social status.

Yes, horses take priority. That's true on nature trails too. Automobiles don't inherit anything from horses and horse-drawn carriages.

Pedestrians existed before carriages, too