1) Not always an occupational term. In the earliest examples quoted in the OED it could be a hunter of game and even a madman or lunatic. In the sense of a workman employed to look after a wood it is noted only from 1426.
However, the following by-name or surname occurred in that part of Kirkburton parish where Roche Abbey had its Timberwood Grange: 1307 Thomas Wodeman, Thurstonland
1324 Adam son of Thomas Wodmen [sic], Fulstone. The role of the woodman is explicit in York: 1390 Ricardus Wodeman ... Willelmus Wodeman ... mensuratores de wode.