"Cold enough to freeze the balls off (or on) a brass monkey" is a colloquial expression used by some English speakers to describe extremely cold weather.

It was widely and incorrectly believed that the Beastie Boys were referring to a different drink made from a 40-ounce container of malt liquor mixed with orange juice ("forty" is mentioned in the lyrics); however, Mike D has publicly confirmed that the premixed Heublein cocktail was their inspiration.

Indeed, there are two different kinds of Brass Monkeys out there: One is a mixture of malt liquor and orange juice and the other is a premixed cocktail “beverage” produced by the Heublein Company in the '70s up until the '90s, that consisted of orange juice, vodka, and dark rum.

Used to describe cold weather, this saying derives from the traditional Navy phrase "cold enough to freeze the balls off a brass monkey". This references the brass structure or 'monkey' where cannon balls were stacked.