Green’s Dictionary of Slang

(drugs) under the influence of heroin or cocaine; thus punning synon. snowed in, snowed up.

c.1925		R. McAlmon Miss Knight (1963) 55: ‘I’m snowbound now, Mary,’ she confided to inform the others that she had just sniffed cocaine.
1927		R.S. Gold ‘Miscellaneous Notes’ in AS III:2 167: Snowed In: Dopey, as if full of cocaine (Snow).
1936		R. Chandler ‘Guns At Cyrano’s’ in Red Wind (1946) 199: He was snowed to the hairline. [Ibid.] 200: That snowed-up hoodlum looked like a life-taker to me.
1949		Monteleone Criminal Sl. (rev. edn).
1956		H. Gold Man Who Was Not With It (1965) 222: I figured on how to get snowed.
1962		P. Crump Burn, Killer, Burn! 323: I got snowed to the gills.
1985		St Louis Post-Dispatch (MO) 1 Sept. 55/1: [headline] Why Are We Still Snowed On Cocaine?