IMO, ancient bowmakers preferred to work with seasoned wood....and some wood, like yew, is easily worked when dry. Green wood is actually hard to work with if you don't have a good cutting tool (like a steel blade). Flint blades are very sharp, but their edges are jagged.....making it hard to get a smooth surface on wood. A seasoned piece of wood can be "sanded" with a course stone to remove the tool marks but a green piece of wood gets "fuzzy" in most cases.
I've read an account that stated that NA's living in dry climates preferred to work on staves cut from dead trees....because mold was not a problem.
In humid climates, I imagine the NA's cut green wood and seasoned them in their lodges before tillering them.