The origin of calling the waiting room a green room has never been discovered. A 17th century Thomas Shadwell play first referred to it: "No madam: Selfish, this Evening, in a green Room, behind the Scenes, was before-hand with me...".
Green rooms could have been green for several reasons: They were painted or decorated green to match scenery on the set. The colour green soothed the actors before and during peformances. Green baize was used as soundproofing the rooms so rehearsals could be held. Green is a corruption of scene or screen, Scene and Screen Rooms being where scenery was stored.
source:the Rec.Arts.Theatre.Stagecraft newsgroup FAQ