The tradition or custom of working, mounting, leading horses from the left side goes back for many years, probably centuries. It started because it was, in those early days, necessary for the rider, handler or the knight to have his right hand free. His right hand was the defensive, or sword, hand and needed to be free for self-defense or battle. That tradition, now completely unnecessary, continues to today.
It is also interesting to note that at the near-ending of the middle ages, the roads in continental Europe were beginning to be straightened (somewhat) and cleared of underbrush and obstructions. Because of this, many “hiding places” for bandits were destroyed so travels became safer. With this change of making roads safer from ambush or robbery, driving was changed from the left side of the road where the driver’s defensive, right hand was needed to be free to the right side of the road so that his right hand could be used for driving or control of his horse(s). The roads in Great Britain were not cleared nor straightened (still are not), so the custom there remained the same. That is why, to this day, the Brits still drive on the “wrong” side of the road.