Premise: The phrase "cold enough to freeze the balls off (or "on") a brass monkey" is a colloquial expression used by some English speakers. The reference to the testes (as the term "balls" is commonly understood to mean) of the brass monkey appears to be a 20th-century variant on the expression, prefigured by a range of references to other body parts, especially the nose and tail.
Hypothesis: The phrase "cold enough to freeze the balls off a brass monkey" is an expression used to describe a very cold climate and NOT to literally mean to amputation of an extremity.