The state addicts are in when withdrawing from drug addiction. Also, predominantly in the U.S.A., plain speaking.
Of course, the term 'cold turkey' in the literal 'cold meat' sense appears many times in recipes - 'cold turkey salad' etc. Neither of the meanings above appear to have any allusory link back to that.
The most common use of the term is now in relation to drug withdrawal. The earliest reference I can find to that is from the Canadian newspaper The Daily Colonist, October 1921:
"Perhaps the most pitiful figures who have appeared before Dr. Carleton Simon..are those who voluntarily surrender themselves. When they go before him, they [drug addicts] are given what is called the 'cold turkey' treatment."
The 1936 edition of American Speech gave a definition of the term:
"Cold turkey, treatment of addicts in institutions where they are taken off drugs suddenly without the 'tapering off' which the addict always desires."
The 'plain talking/getting down to business' meaning of the term is largely limited to the U.S.A. The English newspaper The Daily Express explained that for an English audience in a January 1928 edition:
"She talked cold turkey about sex. 'Cold turkey' means plain truth in America."
There are many uses of the term in U.S. citations from the early 20th century. For example, this from The Oakland Tribune, August 1915:
"This letter talks cold turkey. It gets down to brass."
In the state of drug withdrawal the addict's blood is directed to the internal organs, leaving the skin white and with goose bumps. It has been suggested that this is what is alluded to by 'cold turkey'. That seems doubtful. It is much more likely that the allusion is to the direct, no nonsense approach indicated by the earlier 'plain speaking' meaning of the term.
"without preparation," 1910; narrower sense of "withdrawal from an addictive substance" (originally heroin) first recorded 1921. Cold turkey is a food that requires little preparation, so "to quit like cold turkey" is to do so suddenly and without preparation.
Idioms: cold turkey
Immediate, complete withdrawal from something, especially an addictive substance; also, without planning or preparation. For example, My bad shoulder forced me to quit playing tennis cold turkey, or I'd never done any rock climbing, but decided to try it cold turkey. This term may have come from the earlier expression talk turkey (for blunt speaking). At first used strictly for abrupt withdrawal from drugs or alcohol, it soon was transferred to quitting any habit or activity. [Early 1900s]
Word Origin: cold turkey
By 1922, cold turkey was not always a leftover from Thanksgiving dinner. For an addict, it was quite the opposite. "This method of sudden withdrawall," explained a writer that year, "is described in the jargon of the jail as 'the cold turkey' treatment," It meant "to immediately and completely give up a substance, such as narcotics or alcohol, to which one was addicted."
The shock to the system was such that few addicts voluntarily chose it. "Mention of the 'cold turkey treatment' gives a chill of horror to a drug addict," said Newsweek in 1933. "It means being thrown in jail with his drug supply completely cut off." And Mickey Spillane wrote in I, the Jury (1947), "I doubt if you can comprehend what it means to one addicted to narcotics to go 'cold turkey' as they call it."
This use of cold turkey is an outgrowth of a previous sense, attested as early as 1910, meaning "extreme plainness and directness," going back to talk turkey, attested in 1830. Carl Sandburg used the term this way in a 1922 letter: "I'm going to talk cold turkey with the booksellers about the hot gravy in the stories."
Nowadays going cold turkey is not restricted to narcotics and alcohol addiction. We speak of it as an extreme means of quitting any attachment or habit that we find hazardous to our health: cigarettes, chocolate, a television show, sex--perhaps even a sports team.
Wikipedia: cold turkey
"The etymology derives from the phrase talk turkey, in which someone deals matter-of-factly with a subject. Some, however, believe the derivation is from the comparison of a cold turkey carcass and the state of a withdrawing addict — most notably, the cold sweats and goose bumps. It is often preceded by the verb "to go," as in "going cold turkey."