I’m not a land use expert but from what I’ve seen and dealt with, depending on where you are in the state, most public land is wide open to go into. Generally there’s nothing to stop you from entering via a road or trail. You can drive a forest service road or a dirt road and cross serveral parcels of privately owned, BLM or state owned land. Many of those areas allow people to transit the area to get from one area to another.
As far as a checkpoint like you mentioned thats only state or federal parks that operate to generate funds like Craters of the Moon and the like. Pretty much anywhere else a gate will be closed because its private property and they cannot impede access to an area where theres is an easment to allow movement from one area to another. People try but usually they get told to knock it off. You’ll see alot of that kind of stuff happen on Forest Service roads where somebody decides they don’t want people transiting that road after people have been doing it for 50 or more years.
Most folks hunt, hike, camp and go four wheeling out on those areas. There are areas that I’ve gone into where I was pretty sure our group was the only people for miles. Other areas can be pretty crowded and it’s only getting worse with all the recent transplants. It’s pretty frustrating to hunt in some areas where almost every clearing looks like an RV dealership and people are making enough noise to drive even the cattle herds away. That has become especially frustrating in many areas we’ve enjoyed are getting trashed by all these numbnuts moving here that absolutely no respect for the environment.
If you’re entertaining the thought of moving here one day and buying land, I hope you have really deep pockets and good luck finding a deal. Huge swaths of land have already been bought up and most of the good spots have long since been paid for. Quite honestly everyone and their brother has gotten that idea well before you did. Too many people have watched Yellowstone and think they can still afford to get some land here.
To sum it up, there’s a ton of land here wide open to enjoy, but more and more outsiders are fucking it up, rich people are buying it up, the federal government is closing it up and us locals have to sit and watch it all go to hell.
So good luck to you, maybe Texas isn’t such a bad option.