In fact, you might also say it could "freeze the balls* off a brass monkey". (Which is a bit more vulgar.)
In the UK and US, we use these phrases colloquially to describe exceptionally cold weather.
This usage apparently started in 19th century America. Nobody really knows the reason for the animal mention. But it seems likely that it referred to small brass monkey statuettes of the time (often from Japan). Which were solid metal, and thus fairly impervious. Only very extreme weather temperatures would affect these inanimate simians!
Earlier phrases referred to freezing the whiskers, nose or tail off a brass monkey. The slightly less elegant 'balls' was added in the 20th century!
It seems that a popular, and convoluted, theory of the brass monkey being a tray to store a ship's cannonballs has been debunked by experts as well, balls.
Anyway, brass monkeys is one of English's many strange colloquialisms. And if you hear it when visiting the UK or US, at least you now know what it means ;)
* Balls is UK/US slang for testicles!
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