「雨にぬれる」 Why does it have to be used に in this phrase
I think it's likely this particular phrasing stems from classical Japanese.
If we look for に on http://kobun.weblio.jp we find this:
Essentially, に could be used as a particle to refer to means of action. This helps to account for the "poetic" feeling referenced in the question posted by Chocolate as well as the supposed declining usage of "雨に濡れる" specifically by younger speakers of modern Japanese.