I think you can interpret "Works in woods" as being involved in lumbering out in the forests. There are various tasks involved (such as felling, climbing and limbing trees, attaching chains, hauling with mule teams, etc.), and they may or may not be divided into individual specialties depending on the operation. "Works in woods" is simply avoiding such complications.
The phrase is very unlikely to be used for carpentry, cabinet-making, etc. as the normal terms are more likely to be used, and further, the use of the plural form, "woods", indicates "forest" was meant. If the phrase "Works in wood" had been used, the carpentry interpretation would be more reasonable.