Old English wudu, earlier widu "tree, trees collectively, the substance of which trees are made," from Proto-Germanic *widuz (cf. Old Norse viðr, Danish and Swedish ved "tree, wood," Old High German witu "wood"), perhaps from PIE *widhu- "tree, wood" (cf. Welsh gwydd "trees," Gaelic fiodh- "wood, timber," Old Irish fid "tree, wood"). Woodsy is from 1860. Out of the woods "safe" is from 1792.
"violently insane" (now obsolete), from Old English wod "mad, frenzied," from Proto-Germanic *woth- (cf. Gothic woþs "possessed, mad," Old High German wuot "mad, madness," German wut "rage, fury"), from PIE *wet- "to blow, inspire, spiritually arouse;" source of Latin vates "seer, poet," Old Irish faith "poet;" "with a common element of mental excitement" [Buck]. Cf. Old English woþ "sound, melody, song," and Old Norse oðr "poetry," and the god-name Odin.
Don't worry, that person will not harm you: Answer the question; we won't eat you (1738+)
See FOREST.