Final answer:
The descending hypothalamic fibers are responsible for the sympathetic input of the face.
Step-by-step explanation:
The sympathetic input of the face is controlled by the descending hypothalamic fibers. The hypothalamus, which is responsible for the central control of autonomic function, projects to brain stem and spinal cord structures to regulate the balance of sympathetic and parasympathetic input to the organ systems of the body. Output from the hypothalamus follows the descending hypothalamic fibers, which influence the lateral horns of the thoracic spinal cord.