Usually a mackintosh, but in Canada can be any kind of rain-proof overcoat. One Irish version has it "My Old Surtoo," from a type of overcoat called a surtout.
Yes, one of the Beggarman songs.

An Ulster version, "The Oul' Rigadoo," from Sam Henry's "Songs of the People" was posted in thread 54733: Oul Rigadoo