To revert to manumuskin's question, I, too, have been wondering about the DEP's authority to close these roads. There is relatively recent (2015)
New Jersey case law establishing that "by-roads" are still recognized in New Jersey. A private road that has been used, uninterruptedly, by the public for twenty years, without permission of the landowner, is presumed to have been "dedicated" for public use and thereby becomes a by-road even if the dedication has not been accepted by a public entity.
Barile v. Port Republic made it clear that the public right of passage along a road can't be extinguished by an administrative act of a municipality (which may, or may not, be obliged to maintain it). Once right of passage has been established, it can only be abolished by the passage of a municipal ordinance vacating the road, promulgated with due notice and hearings, etc.
Now, for things like plowed firebreaks and so on, I feel like it would be difficult to establish the twenty years of public use, and the DEP would probably be able to show that they'd taken action to interfere with public use (rebutting the presumption this this was a public road). But I'm at a loss to explain how the DEP could have authority to unilaterally close, say, a part of the Tuckerton Road, without the municipality vacating it. The fact that it lies across their lands is immaterial; the public's right to that road was already established when the Wharton Estate conveyed it to them.