Green’s Dictionary of Slang

cozy adj.

(US) drunk.

1853

Ohio Organ (Cincinnati, OH) 28 Jan. 13/2: Dr Franklin speaking of the intemperate drinker says [...] he may be boozy, cozy, foxed [...] groatable [...] may see two moons [...] pretty well entered, but never drunk.

In phrases

play it cozy (v.)

(US) to hold back, to act carefully.

1974

R. Dennis Working for the Man in Complete Hardman 976: ‘He calls you at eight-fifteen. But [...] you’re playing it cozy. [...] You ask him to prove he’s got a copy’.