Are you sure you’ve exhausted all options for running the cable inside the house? Such as: beneath carpeting, behind baseboards, around and behind door trim, through attic or basement…
I’ve never heard of doing this outside, but people do have outdoor speakers, so it’s not really a new concept. You just need to ensure the wire is protected from the elements. I’m not sure where the idea of Cat6 came from, but I’m pretty sure normal speaker wire will hold up to weather much better than ethernet.
