Final answer:
The nuchal ligament is the term for the structure extending from the poll to the withers, supporting the horse's head by connecting cervical vertebrae to the skull.
Step-by-step explanation:
The anatomical term for the ligament that extends from the poll to the withers of a horse and helps support the horse's head is the nuchal ligament. This ligament is part of the supraspinous ligament which, in the posterior neck, expands to interconnect the spinous processes of the cervical vertebrae and attaches to the base of the skull, specifically out to the external occipital protuberance. It plays a crucial role in supporting the head and preventing it from falling forward, particularly in quadrupeds like horses and cows where this structure is much larger and more robust to accommodate their larger skulls. It is an expanded portion of the supraspinous ligament in the posterior neck. The nuchal ligament attaches to the cervical spinous processes and extends upward and posteriorly to attach to the midline base of the skull.