Welcome aBoard, nemo. Confess I have never heard of where
you're from.

A woods does sound odd, doesn't it? But it's common, though we do say a forest.

(Oh, dear--I had a whole paragraph of what I thought at the time was a sensible explanation, until I re-read it. I'm going to let somebody else take over, and go try to straighten out the tangled scramble of my brain!)