That's the first time I've encountered "a woods" too. We already hae "a links" and "an innings", but in these cases the original singular is not used. With woods we can refer indifferently to the same place as either a wood or woods, so with "the" or proper names such as Highgate Wood(s), they seem to be synonyms syntactically as well as semantically.

"Wood" is related to "divide" and "widow", its original meaning being a separating stand of trees