I'm betting a lot of you did a search on the origins of this term. What you found is that there is some disagreement about the true origin, but isn't that true of so many of our sayings. The nautical version is the one that gets the most attention and is a family friendly version.
I found this same reference used online and credited to numerous sources, so I'll just say it isn't mine.
"Brass monkeys or brass monkey weather – Very cold weather, origin from the cannon balls being stored on a wheeled platform (monkey) made of brass. If the weather was so cold as to cause cannon balls to fall off the brass monkey due to different shrinkage rates of the dissimilar metals it was termed to be cold enough to freeze the balls off a brass monkey."
I love this version of the term and as far as I am concerned it is the only true one out there.