I think "they" can do whatever they want.
My interpretation of the scant info is that you would need some kind of permit and sticker on your windshield to drive on the unpaved roads on state land. I believe other states have this, years ago I was passing through Maryland(?) and took a little detour through a state forest. There were signs saying you needed a permit to drive on those roads and would be fined without one. I was only there for an hour or so, but nobody asked to see my permit, LOL.
So, who knows, if they passed a law like that I wouldn't be especially happy but I'd just get the permit. I mean, what could they charge? $50? If they actually used that money to enforce existing laws or improve the state forests then it wouldn't be such a bad thing. I just avoid Wharton now, haven't been there in awhile, but from posts I see here it sounds like there are a lot of park police and getting a ticket would probably be a lot more expensive than the permit. For that matter, they could make it a license plate sticker and use automated cameras to check for compiance. That would likely generate a lot of income from un-permitted users.