No, I see that GG ~ but my point was that, within the context of this imperfect [in the sense of incomplete] variant of the song, does it not imply recollection of his reason for having passed her his overcoat in the earlier, more complete, versions?

(Actually, GG, if you are out in cold weather, do you go around offering your coat to anyone who has chosen not to dress quite so warmly as yourself? I should call that very unusual behaviour unless there was some obviously drastic underdressing [such as nakedness!] apparent?)