The song is the "Swallow song of Rhodes", an ancient Greek folk song preserved by the rhetorician and grammarian Athenaeus who lived during the 2nd century CE. It was performed by the children of Rhodes as they went from house to house, maybe dressed up as swallows or carrying a wooden swallow on a stick, in what seems to have been an ancient version of "trick or treat". Because of the theme of the song, this is mostly believed to have taken place in springtime. The swallow was seen as the bringer of spring. But Athenaeus says that it took place in the month of Boedromion, and in Athens Boedromion was an autumnal month.
Maybe Boedromion came in the spring on Rhodes or maybe, as Pär Sandin professor of Greek at the University of Bergen suggests, the reality behind the song is grimmer than we have realized. "In the later European context, ‘trick-or-treat’ indeed took place in the autumn, after the harvest and slaughter was done, when farms and houses were well-stocked. The poor people who performed the trick-or-treat had long winter months to look forward to, and needed every ounce of nutrition they could get. [...] What if the talk about spring and beautiful seasons is only a game, a sort of grimly humourous joke intended to soften the hearts of the rich mansion-owners — and, at the same time an instance of the superstitious euphemic practise so common of Greek society. The beautiful season, which is coming, is not the spring — but winter. Let’s call the winter beautiful, maybe it will be nicer to us".