When we ride, or drive horses, we have control over the horse's head through the head stall. Depending on the task we want the horse to do, the head stall can be a halter or bridle with or without bit.
But the term "the head leads and the body follows" has also a psychological bearing, the brain leads and body follows. Training and education is a coin with two sides, a physiological and a psychological and to get the best effect of training and education these two needs to coincide.I found an image illustrating the two sides of the coin in Hans von Blixen Fineckes book The Art of Training.
Hans von Blixen-Finecke talking about riding as a language of touch and a prerequisite for this form of communication is calm, within both horse and rider. Calm and presence.
A friend who has vast experience of riding young race horses think the most important thing in any form of training of horses is that the horse never gets frightened during the early training. It gets a positive attitude to the rider and the work it should do, it will feel safe and it makes the psychological side of the coin interact with the physiological in a beneficial manner. A calm horse can digest information from the rider, a scared and nervous horse is blocked.
Another friend was at a jumping competition at the weekend and reported with a tired tone that few were actually riding, most engaged in trying to control flight responses with both bit, extra reins and BF&I (brute force and ignorance). The BF&I riders had certainly gained control over the horse's head mechanically but they had totally missed getting the horse mentally.
It is important for us as riders to be in a good balance within ourselves. As we sit on the horseback our own internal weight distribution (skewness) affects the horse's body. Somehow the horse must handle adding our weight to its own and distribute it over his feet. The more equilateral and straight we are aligned around our own spine, the more even our weight is distributed to the horse.
When we ride, and I assume that we are aware of our own bodies, it is the shift in the horse's balance we feel through both seat and hands. The shift signals to us if the horse is in a good self carriage in the current movement.. An untrained, uneducated or a horse that is under rehabilitation have more obvious shifts in the balance than a healthy and more educated horse. By being present in each step, we as riders are able to feel how the horse move and we can with our signals, our touch, give aids that help the horse to place the weight and regain balance.
A good education ultimately leads to an equipage that makes everything look easy, it's two brains joined in movement and although it is the rider who leads it is the sence of trust developed in the relationship that makes the horse participate without fear. At this point the rider can be said to ride the horse's conscious brain and in that context, the rider, if the he/she would like, can remove all the equipment from the horse and ride on.