I think this is supposed to be a parody/homage to something, but I'm not sure what. I can think of a couple of showtunes that are similar to this song.
Part of me is saying, "Gee, Bert, what's it to you if those kids want to wear their galoshes on their heads, etc.?" But then I think, dressing appropriately for winter can be a matter of life or death, so I suppose it would be irresponsible of him not to at least say something.
I'm overthinking things again, aren't I? I do that.