Step 1: Understand Horner syndrome. Horner syndrome results from interruption of the sympathetic supply to the eye. Its classic triad is partial ptosis (drooping upper lid), miosis (constricted pupil), and anhidrosis (loss of sweating) on the affected side, often with apparent enophthalmos.
Step 2: Identify the muscle causing the ptosis. The upper eyelid is elevated by two muscles: the Levator Palpebrae Superioris (LPS), a skeletal muscle supplied by the oculomotor nerve (CN III), and the superior tarsal muscle (Müller's muscle), a smooth muscle that receives sympathetic innervation. In Horner syndrome the sympathetic supply is lost, so Müller's muscle is paralysed, producing the characteristic partial (mild) ptosis. Hence Müller's muscle is responsible.
Step 3: Why the other options are wrong. Orbicularis oculi is the lid closer (supplied by the facial nerve); its paralysis causes inability to close the eye, not ptosis. Levator palpebrae superioris is the main elevator but is supplied by CN III, not the sympathetic system; its paralysis causes a complete ptosis (as in third nerve palsy), not the partial ptosis of Horner syndrome. "Horner muscle" (the lacrimal part of orbicularis oculi, pars lacrimalis) is concerned with tear drainage, not lid elevation.
Final answer: Option D - Müller's muscle (superior tarsal muscle).