Trace the innervation, then the muscle follows. Horner syndrome is fundamentally a sympathetic denervation of the eye. So the muscle responsible for any feature of Horner syndrome must be a sympathetically-supplied muscle.
Apply this to the eyelid. The lid is held up by two elevators:
• The big skeletal elevator, Levator Palpebrae Superioris, runs on the oculomotor nerve (CN III) - not sympathetic, so it is spared in Horner syndrome.
• The small smooth-muscle elevator, the superior tarsal muscle = Müller's muscle, runs on sympathetic fibres.
When sympathetic input is cut, only Müller's muscle weakens. Because it contributes just a few millimetres of lift, its loss gives the characteristic mild/partial ptosis of Horner syndrome (in contrast to the severe, complete ptosis of a CN III palsy that takes out the levator).
The remaining options fail on function or nerve supply: orbicularis oculi closes the lid (facial nerve); the so-called Horner muscle is the tear-pump part of orbicularis, unrelated to elevation. Therefore the muscle producing the ptosis is Müller's muscle (Option D).