Bembo's depiction of this card has always struck me as melancholy. He seems slightly cross-eyed, a simpleton. We pity the fool.
It is hard to know if the feathers are placed there by mockers, or because he has had to sleep in barns with the chickens, having no place of his own. His stick would be as much to beat the dogs who chase him as to carry his belongings. Every one who walks in the country must carry a stick.
I don't know about the Lent connection - this was indeed Moakley's thesis, at least a working theory that let her tell a story. It depends upon the other part of her theory being true - that the Bagatella depicts a Carnival King. I think most interpreters regard her theory as far-fetched nowadays. But there is an iconographic tradition of portraying Fools like this, as Giotto's famous frescoes show. The same kind of icon for "Stultitia" (foolishness, stupidity) is found in illuminated manuscripts of the Bible in Psalm 53 - "The fool has said in his heart 'There is no God'". So the Visconti icon of foolishness stays close to traditional depictions.
He is the "lowest of the low", but I think another way to look at it is that he actually has *no place* in society. He is an outcast with no fixed address, no fixed position, which is presumably why the game designer choose a Matto - a nut, idiot, fool - to represent the card with no fixed place, that could stand in for any other at least once. So he is nowhere, but he could be anywhere.
It is perhaps impossible to recover the original role of the Matto in the game - whether he is like the "excuse" in French tarot for instance - but I think the imagery gives a clue, that he was played like this - with no fixed place in the order of counting the trumps. Since Il Matto cannot be counted in any position, the deck is never finished - a provisional state of it can only be reached in play.
Like in French to this day, which does not distinguish between "jeu" meaning "game" and "jeu" meaning "deck of cards", the earliest Italian descriptions used the words "gioco da carte" ("zogo" in some dialects) to mean both the deck and the game (now Italian like English distinguishes the game played from the physical object, the deck, with "mazzo"). The deck therefore *is* the game, always unstable because of this card.
In the Visconti-Sforza, Il Matto is also a natural fool - as opposed - stunningly - to the d'Este and Bolognese cards, where he is a professional fool. But in both cases a fool - one a vagrant, as the later TdM would seem to have it, the other an entertainer. Perhaps the two depictions meet in the idea of wandering, with no fixed place, and fools can either choose to entertain, or they can be unwitting entertainment.
We might think the Sforza court was a more serious place than the Este court, given this depiction of the Matto. I don't know if Bianca Maria and Francesco Sforza's court had fewer professional fools than Ferrara, but Sforza's successor, his son Galeazzo Maria, loved them - just as his contemporary in Ferrara, Borso d'Este. Perhaps if this deck had been made for Galeazzo Maria, his Matto would be juggling or doing something else to entertain the crowd, rather than being an outcast from society.
Finally, looking closely, we can see his pubic hair. This allusion to his nudity is shared with the "Charles VI" Matto, where children are trying to pull down his loincloth. Our Matto's nudity brings us close to his weakness, his helplessness, lack of position in society, and his utter dependence on God - or fortune. His rags, nearly revealing his nakedness, allows the madman to be the closest reflection of the true human condition in among the trumps - alone, weak, poor and nearly defenseless, a stranger. "Who told you that you were naked"? says God to Adam and Eve; and the rest of the people in the trumps appear in various sumptuous guises, but (excluding a few cherubs and cupids) we will not see this nudity again until the end of the series, the Judgement, when even the rags will be thrown off.
Even taking into account the difference between ending the series with the Mondo (World) or the Angelo (Angel or Judgement), it is amazing how the TdM preserves the allusion to nudity at the beginning and the end, just as the Bolognese or Eastern order applied to the Visconti-Sforza and Cary-Yale (the latter has a full nude figure); and the Charles VI deck illustrates this correspondence perfectly - the highest card l'Angelo has many nude figures climbing from their graves, unashamed now, perhaps because unaware, of their human frailty. The stultitia of the simpleton, almost perfect but covered in rags, has become glorious wisdom, the fully revealed, knowledge of God.