Someone who hunts animals in a wood, hunter, huntsman.
Someone who cuts down trees or cuts and sells wood, lumberjack, woodcutter.
Someone who lives in the wood and manages it; a woodsman; (by extension) someone who spends time in the woods and has a strong familiarity with that environment.
Someone who lives in the woods and is considered to be uncivilized or barbaric, a savage.
Someone who makes things from wood.