Green’s Dictionary of Slang

grass; thus send to Dr Green, to put a horse out to grass.

c.1786		Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Green. Doctor Green. Grass. frequently recommended as the best Cure for most Diseases to which Horses are liable.
1788, 1796		Grose Classical Dict. of the Vulgar Tongue (2nd, 3rd edn) n.p. Doctor Green; i. e. grass: a physician, or rather medicine, found very successful in curing most disorders to which horses are liable. My horse is not well, I shall fend him to Doctor Green.
1811		Lex. Balatronicum.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.
1826		Vulgarities of Speech Corrected n.p.: He has sent his horse to Dr. Green, He has put his horse to grass.