Green’s Dictionary of Slang

(orig. US black) milk.

1940		Waukesha (WI) Freeman 24 Jan. 3/3: ‘Guernsey highball’ or ‘moo juice’ – milk. [...] ‘Brown moo juice’ – chocolate milk.
1944		Cab Calloway New Hepsters Dict. in Calloway (1976) 258: moo juice (n.): milk.
1965		E. Bombeck At Wit’s End (1979) 156: I had a fetish about the kids drinking their moo-moo from any cup that didn’t have their name on.
1970		E. Thompson Garden of Sand (1981) 304: Get the kid a horsecock and cheese sandwich and some moo juice.
2005		Daily Mirror 17 Mar. 🌐 Celebs such as Jennifer Aniston, Britney Spears, Sarah Michelle Gellar and Tess Daly have all been seen guzzling a long, cool glass of moo juice.