Green’s Dictionary of Slang

cold enough to freeze the balls off a brass monkey phr.

also freeze a brass monkey, ...the ears off a brass monkey, ...nose..., ...tail..., to blow the balls off..., freeze the tail off a tin possum, make a Jew drop his bundle, snappy enough to freeze the plumbing off a brass elephant

[mid-19C+] (US/Aus.) of temperature, extremely cold; also fig. use.