The lyrics you quoted are a Mother Goose rhyme that go like this:
The north wind doth blow, And we shall have snow, And what will the robin do then? Poor thing!
He'll sit in the barn And keep himself warm, And hide his head under his wing. Poor thing!
I never knew the melody that goes with it, but I always enjoyed reading it to my children. I always read it with a British accent, kind of like an Allistair Cooke voice.