>I believe the British version is "out of the wood"?

You could be right, although I have only ever heard "out of the woods".

Regarding the rest of this thread, I have never heard anyone say "a woods" only "the woods" although now I think about it, people do talk about "a wood" sometimes. I wouldn't be surprised by the following usage "how about visiting a local wood to look at the flora and fauna?" I supppose it is a matter of context to avoid confusion with wood as in woodwork.