When a horse is moving, your body should be allowed to move with the horse in order to stay in balance. This is one of the big advantages of using horses for physical therapy. The person sitting on the horse's back must be constantly adjusting to stay in balance. In watching therapeutic riding, one can often observe the rider's muscles become softer after the first few minutes because of this constant movement of the muscles. It is almost like getting a free massage in addition to the riding.
Tense muscles may be a result of mental tension, holding one's breath, bracing against impact, or trying to hold on to the sides of the horse. Tense muscles slow one's reaction time. They also cause the muscles to exert more effort than necessary to effect movement. This excess effort may, also, cause over-reaction.
When standing in the stirrups, it is important to keep one's weight centered over the stirrups or they will swing. Slight pressure of the leg against the horse may help stabilize a rider, but it is best to let the natural shape of the horse's body create this pressure.
A rider may lower his center of gravity by inclining his upper body forward. When doing this, however, he must flex his legs and move his rear backward to remain in balance.