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The question is:
Q: What mysterious Flemish peasant activity is depicted in this painting?
and one guess was:
Q: There is this activity he depicts in the background... It looks like shooting arrows at a pole - but that doesn't seem to make much sense.
And curiously, this is exactly it.
The group is playing a game: shooting at a popinjay:
Popinjay or Papingo (signifying a painted bird), also called pole archery, is a shooting sport that can be performed with either rifles or archery equipment. The object of popinjay is to knock artificial birds off their perches. […] The archery form, called staande wip[circular reference] in Flemish language, is popular in Belgium […]
With Wikipedia bringing us two pictures as examples, first Tir à l'arc au papegai:
[
and the following picture 'Popinjay mast for archery in Havré Belgium' as an example:
This example in turn matches the echo master Bruegel himself presents us with, this time unused for sports and fun, just standing there in the background, in the painting "Hunters in the Snow" (empty field, vertically centred, extreme right):
zoomed in:
Two more Wikimedia commons pictures with a more matching configuration of shooters compared to the painting:
and how it evolved:
This solution is confirmed by:
It is the calendar’s festivity of carnival in Gloomy Day that balances out the prudent tasks of early spring: at the right, the little carnival king in his printed paper crown watches the adults happily eating waffles, while in the opposite corner of the scene, down in the village, another family dances in the street outside an inn. In the next remaining scene of the series, Hay Harvest (June/July […]), the festive moment is very distant and yet, characteristically, fairly central on the panel: on a village green, people have gathered for a competition involving shooting at a popinjay on a pole. This pole also stood in an empty, snow-covered village green beyond the frozen ponds in Hunters, one of the echoes in the series that gives a sense not that we see the same place, but that every place we see is somehow archetypal, universal. In Hay Harvest Bruegel gestures to the universality of the view by structuring his composition as a clear echo of the ‘world landscapes’ of Joachim Patinir, some forty years earlier, with the colour scheme moving carefully from foreground brown to green to distant blue, the rather choppy sense of space where roads fail to connect individual features, and the great inhabited rock formations jutting suddenly upward from pleasant farmland.
— Elizabeth Alice Honig: "Pieter Bruegel and the Idea of Human Nature", Renaissance Lives, Reaktion Books: London, 2019. (gBooks)