Much of Frost's poetry is about Vermont or New Hampshire, and Vermont's private woodland is very open (except in a few towns) and has always been so. This is thanks to the Vermont Constitution's provisions on hunting:
The inhabitants of this State shall have liberty in seasonable times, to hunt and fowl on the lands they hold, and on other lands not inclosed... under proper regulations, to be made and provided by the General Assembly.
If land isn't fenced off or actually posted (and posting large woodlands is deliberately difficult in Vermont), then it doesn't count as "inclosed."
And Vermont's culture still supports this. There are hundreds of acres of unposted private land near my house which are owned by old-school Vermonters, and I am absolutely welcome to hike them.
Maine has a slightly different set of rules, and posting land is easier. But once you get away from the coast and into the serious forest, it's not that different from Vermont. And as far as I know, New Hampshire also allows hunting on unposted woodland.