The Collaborative International Dictionary of English v.0.48:

Woodman \Wood"man\, n.; pl. Woodmen. [Written also
   woodsman.]
   [1913 Webster]
   1. A forest officer appointed to take care of the king's
      woods; a forester. [Eng.]
      [1913 Webster]

   2. A sportsman; a hunter.
      [1913 Webster]

            [The duke] is a better woodman than thou takest him
            for.                                  --Shak.
      [1913 Webster]

   3. One who cuts down trees; a woodcutter.
      [1913 Webster]

            Woodman, spare that tree.             --G. P.
                                                  Morris.
      [1913 Webster]

   4. One who dwells in the woods or forest; a bushman.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Woodsman \Woods"man\, n.; pl. Woodsmen.
   A woodman; especially, one who lives in the forest.
   [1913 Webster]

WordNet (r) 3.0 (2006):

woodsman
    n 1: someone who lives in the woods [syn: woodsman, woodman]
    2: makes things out of wood [syn: woodworker, woodsman,
       woodman]

Moby Thesaurus II by Grady Ward, 1.0:

31 Moby Thesaurus words for "woodsman":
   arboriculturist, backwoodsman, briar-hopper, brush ape, bushman,
   clam digger, conservationist, cracker, desert rat, forest ranger,
   forester, frontiersman, hillbilly, hinterlander, logger,
   lumberjack, lumberman, mountain man, mountaineer, piny, ranger,
   redneck, ridge runner, silviculturist, timberman, tree farmer,
   wood chopper, woodcraftsman, woodcutter, woodlander, woodman