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 send him to Doctor Green.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Greek * Green-1Nathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes