"She hasn't said but a few words to me..." or "She has said but a few words to me..."?

Just as you do, I hear,

"She hasn't said but a few words to me since last winter."

as meaning the same as,

"She hasn't said anything but a few words to me since last winter."

Going on that, I'd say the former is correct, but tentatively, as I don't know exactly where that split in usage happened. I also differ with your common-use anecdote in that I believe the former to be more common in that context. But such is language.

I would use the second; "She has said but a few words to me since last winter."

This means "she has only said a few words to me since last winter".

"She hasn't said but a few words to me since last winter" doesn't really mean anything at all.