It seem to be wholly overlooked, apart from the side-note by
Tolkien.
A part of the Dúnedain of Cardolan most probably would have merged themselves with their counterparts in Arthedain, (note 'faithful Dúnedain' some may have switched sides, such treacheries have happened before, as
Elrond states) and some of them may have eventually left
the Old Forest to join their counterparts in
Lindon.
And though
Angmar was subdued by
Elves from Lindon,
Lothlórien and
Rivendell but during the reign of Argeleb II (Araphor's son) the great plague had ravaged the remnants of the Dúnedain of Cardolan.
Major deforestation? Given the aggressive nature of the
trees in the old forest and their possible friendship with
Bombadil it is doubtful as to whether they would or would need to deforest the Old Forest. Although the
Northmen de-forested a lot of Eastern
Mirkwood (East Bight) a lot of
men could live in forests without the need to deforest them.
Khazad-Bombadil seems to understand Old Man Willow's purpouse's pretty well.