Woolsey
“A wood sawyer or cutter,” based on the Middle English wold (wood) and sawe (saw).
Woodman
“A woodsman,” i.e. one who works in the woods as a woodcutter, trapper, etc. Based on the Middle English wode ( a forest) and man (a man).
Woodley
“From the meadow near the wood,” based on the Middle English ivode (a wood) and ley (meadow). Also spelled Wodeley.