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'. There's no evidence to support that view. So read about the other theories as to the origin of this phrase here.
Apparently cold turkey started off as "talking cold turkey" - which I have never heard of, you? And it meant, or means, talking plainly. But nobody knows why a turkey is a metaphor for talking. ???
So it seems this idiom is a bit of a mystery in origin and purpose. When it is used today it is to indicate someone coming off of an addictive substance or habit.