Green’s Dictionary of Slang

moist n.

[play on damp n. (1)]

(US) an alcoholic drink, thus moist drink.

[UK]‘Pot’ & ‘Swears’ Scarlet City 544: Charlie, come and mash me for a bit, my Johnny’s gone to get a toothful of moist.
[US]C.L. Cullen More Ex-Tank Tales 40: My friend was still riding and purchasing Gallic moists.
[US]Hickman Courier (KY) 12 Nov. 5/6: The manufacturer is making an effort to introduce it in territory where the ordinary moist drink is prohibited.

In compounds