Reference > Brewer’s Dictionary > Near Side and Off Side.

 Near,Neat as a Bandbox. 
Near Side and Off Side.
Left side and right side. “Near wheel” means that to the coachman’s left hand; and “near horse” (in a pair) means that to the left hand of the driver. In a four-in-hand the two horses on the left side of the coachman are the near wheeler and the near leader. Those on the right hand side of the coachman are “off horses.” This, which seems an anomaly, arose when the driver walked beside his team. The teamster always walks with his right arm nearest the horse, and therefore, in a pair of horses, the horse on the left side is nearer than the one on his right.   1
   Thus, 2 is the near wheeler and 1 the near leader, 4 is the off wheeler and 3 the off leader.   2

 Near,Neat as a Bandbox. 

