How can I explain horse drawn carriage using vectors?

A horse exerts a force F backward along AD at an angle to the horizontal with its foot on the ground while walking. According to Newton’s third law, the ground also exerts a uniform reaction force F along GC on the horse. The reaction force is divided into two parts. One component is Fsin$ along the vertical, acting against the horse’s weight, and the other Fcose$ along the horizontal, which propels the horse forward.