Horses require what yoga does: control.
There must exist a perfect balance between force and ease, calm and storm.
With horses, the rider shares his energy with his mount. If the rider is angry or anxious, the horse will embody these feelings. It may spook or act out, turning butterflies to pterodactyl dragons and arena exercises into rodeo shows. If the rider is happy and calm, the horse will embody these feelings. It may brave dark pond waters or overcome next level jumps.
On the mat, the yogi must moderate his energy within and outside of himself. If he is angry or anxious, his session will turn out accordingly. He may fall or give up, unable or unwilling to continue to hold a pose or complete a movement. If the yogi is happy and calm, his session will turn out accordingly. His body may tremble, but he may pass through the rhythms and cycles of his sitting.
What you exude going in is what may exude coming out.