"Couldn't stop a pig in a passage" is the version I know. Anyway...

It's cold enough to freeze the balls off a brass monkey... came from the 18th century British Navy.,,, They had monkeys (square racks made of iron and designed in squares to hold 16 cannon balls). However, when in icy conditions, the iron was subject to shrinkage and the cannon balls rolled off onto the deck. Subsequently, brass monkeys were made which actually worked well..... but the expression, it's enough to freeze the balls off a brass monkey was coined.

Utter rubbish, I'm afraid, GSilver! ;-) It's certainly a popular & widely known explanation for the phrase, but it's not remotely true. It's actually a good example of Meself's most 'explanations of common phrases' turn out to be highly dubious...

I can't give you an elegant explanation of the whole why & wherefore of this, because I've not yet completed the entry (I write an occasional "Word of the Day" thing for a group of friends, but have had no time lately to complete any of several nascent pieces). But consider these things...

The more common version of your explanation is the monkey was a brass frame on which cannon balls were piled pyramid fashion, and the difference in the rate of expansion / contraction would result in cannon balls being popped off the frame in cold weather.

First a ship of the "Wooden Walls" era is very much subject to the whims of the weather. You wouldn't store cannon balls in this fashion; they'd quickly be rolling all over the decks, and you don't want 12-, 24-, 36-lb lumps of iron doing THAT! Also relevant is that you don't want iron cannon balls exposed to the elements - they rust (another reason why it wouldn't have been an iron frame; they'd potentially rust themselves together). Gunners actually took the trouble to remove any imperfections on the surface of a ball, as otherwise it might not fly true when fired, or even jam in the barrel & cause the gun to explode.

Second, one gentleman on the net pointed out that if the “monkey” were your dimpled frame (rather than just a square) a yard across, to move a 6” ball 1”, given the relative expansion & contraction of iron & brass, the temperature would have to fall to some -4,000,000 C. Which is going to be tricky to achieve given that Absolute Zero -273.15C is the theoretical zero point of temperature (0 Kelvin), from whence it is not possible to get colder. So physics as well as practicality is against it.

Third, other monkey expressions are scald the throat, singe the hair, melt the nose; freeze the tail, nose, ears, whiskers. The good old OED lacks any reference to the phrase being used in this way. It's entirely possible that the one time popularity of the "Hear / see / speak no evil" ornamental trio of monkeys, usually made of brass, has given precedence to that version of the phrase above the the others. Whilst an amusing tale, historical it most certainly is not!*

* Historically speaking, the RN used shot garlands - wooden planks with holes bored into them; a lot easier & cheaper to make in those days than expensively casting metal...