To complete above info re Red Wing: the music is as stated by K Mills; when sung, words are by Thurland Chattaway. Much parodied, of course, as 'The moon shines bright on Mrs Porter {whose daughter for some reason washed her feet in soda [or dirty] water}', a scurrilous WW1 soldiers' version quoted by Eliot in 'The Waste Land', & also by Ernest Raymond in his once-popular WW1 novel 'Tell England'; and also as 'The moon shines bright on Charlie Chaplin, his boots are cracking for want of blacking' &c - also from WW1 period, as it sends Charlie in the last line to "The Dardanelles", which crops up IIRC in Joan Littlewood's "O What a Lovely War".

But I agree it is originally about a girl, {"There once was an Indian maid"}, who loses her lover in battle; and not a [feathered] bird.