The hypothalamospinal tract is a nerve tract that arises mainly from the paraventricular nucleus of hypothalamus, and lateral and posterior areas of the hypothalamus. The tract descends through the periaqueductal gray and adjacent reticular formation. It is found in the dorsolateral quadrant of the lateral funiculus, in the lateral tegmentum of the medulla, pons and midbrain.

The hypothalamospinal tract includes fibres by which the hypothalamus projects to the ciliospinal center in the spinal cord, a part of a brain circuit regulating pupillary dilatation as part of the pupillary reflex. 

Lesions of the hypothalamospinal tract cause ipsilateral Horner's syndrome.

References 

Hypothalamus
Brainstem
Central nervous system pathways