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I am writing in regard to a paper by Drs. Weinstein and Langham in the October 1969 Archives (page 483) entitled "Horner's Syndrome and Glaucoma." In this article the authors indicate that in their patient the glaucoma was less severe on the side which had the Horner's syndrome.
In my practice I have a patient who has a right-sided Horner's syndrome and bilateral glaucoma and this patient also has definitely less severe glaucoma on the side of the Horner's syndrome.
Although it could just be coincidence that the glaucoma is milder on the side with the Horner's syndrome, it is an interesting suggestion that the Horner's syndrome may to a degree protect an eye from glaucoma.
Harper JY. HORNER'S SYNDROME AND GLAUCOMA. Arch Ophthalmol. 1970;83(3):383. doi:10.1001/archopht.1970.00990030383022