The popular Q&A site "AllExperts" dates the phrase back to 1910 and states that it originally meant "without preparation," referring to the ease of making a dish of cold turkey. In 1922, the expression acquired its darker connotation related to drug withdrawal.

The state addicts are in when withdrawing from drug addition, especially heroin. In the state of drug withdrawal the addicts blood is directed to the internal organs leaving the skin white and with goose bumps.

From wikipedia - The term allegedly derives 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."

Some say it's because heroin addicts undergoing withdrawal are so pale and covered with goose bumps their skin looks like that of an uncooked turkey. As with most good stories, however, this appears to be crapola. "Cold turkey," which dates from 1916, is related to "talk turkey," meaning to cut the comedy and talk frankly. Similarly, when you go cold turkey, you dispense with the preliminaries and get right down to it. Why turkey rather than crested titmouse, say, is not clear, but perhaps it was because the turkey, as your standard U.S. game fowl, recalled the no-bull simplicity of frontier life. http://www.straightdope.com/classics/a3_269.html

You get goose bumps on your skin, like on a cold turkey.

And another similar explanation from the Word Detective: Dear Evan: Could you please tell me where/how the following two phrases originated? "Cold turkey," as in stopping a habit suddenly, and "On/off the wagon," as in drinking. -- Ken Shifman, via the Internet. Good evening, ladies and gentlemen, and welcome to Bad Habits Week in the wonderful world of words. For some curious reason, a high percentage of the questions I've been receiving lately have dealt with phrases associated with drunkenness or other "substance abuse" problems. Well, it is still early in the year -- perhaps everyone's New Year's resolutions just collapsed. I don't make New Year's resolutions myself. I just re-define all my bad habits as family traditions, which makes continuing to practice them seem downright virtuous. To "go cold turkey," meaning to stop using an addictive drug suddenly and completely, usually incurring extremely unpleasant symptoms of withdrawal, is a phrase which dates back to the beginning of the 20th century. "Cold turkey" is actually based on another colloquial phrase, "to talk turkey" (sometimes "to talk cold turkey"), meaning to face unpleasant truths squarely. It's not entirely clear how turkeys came to be associated with honesty and straightforward confrontation of difficulties, but it may simply be that turkey farmers were renowned at one time for their lack of pretense and blunt speech. The "wagon" in "on the wagon" (having sworn off drinking all alcohol) and "off the wagon" (having failed in one's resolve and thus having started drinking again) refers to a fixture of America's past, the water wagon. Before roads were routinely paved, municipalities would dispatch horse-drawn water wagons to spray the streets in order to prevent the clouds of dust that traffic would otherwise cause. Anyone who had sworn abstinence from alcohol (and would presumably be drinking largely water from then on) was said to have "climbed aboard the water wagon," later shortened to "on the wagon."