With new advents agricultural production started to rise transportation of crop became problematic. Immediate solution in US and Denmark was carts being pulled by multiple horses (higher horsepower, quite literally). The wagons did not have a seat and again, majority of right handed men decided to follow right hand convention. Going from right hand side of the road one could -
ride the rearmost horse on the left, leaving right hand free to whip horses.
easily monitor oncoming vehicles and their wheels which are coming from the opposite side