Using "the" before cold weather seems to emphasize the description of a specific period of bad weather during some time in the past:I was exposed to the rain and the wind, and the cold weather tended to shorten battery life.Without "the" it becomes a more general statement (i.e. cold weather with or without the rain and wind):
I was exposed to the rain and the wind, and (x) cold weather tended to shorten battery life.
(I do have a question that doesn't really affect my response but might make things clearer: Is the subject of the sentence supposed to be "it", referring perhaps to a car or a phone or something else with a battery...?)
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