I've only walked trails in Brazos Bend so I'm not sure about 4-wheel-ers, UTVs, etc. It is, however a fun place to go if you like BIG (10'-13') gators. Just don't take your dog along; it well could be a one-way trip for him. And watch your step - the gators are NOT docile.
If you're down in the Freeport/Surfside/Lake Jackson area, there are places along the Freeport levy one could ride. Lots of swamps but few trees and trails. Again, watch for gators out there.
Then there's Bolivar Peninsula. The danger there are the babe's in bikinis or those getting their full body sun tans.
I do recall a seldom used motocross track out around Hitchcock. And there's Rio Bravo on the north side of town. Both of those are maintained tracks so to speak, and have some sort of entry fee. I haven't actually driven or rode on either of those though.
Sam Houston was always my favorite. There definitely are some wilderness areas in Sam Houston. There are a few marked trails maintained by the San Jacinto Riders, and many unmarked trails. Take a compass and spare fuel if you go there. Your IN the Big Thicket there. Son & I came very near running out of fuel (and totally lost) on dirt bikes in there. The Fun Meter will absolutely blow up in Sam Houston if you'll get away from the camp grounds.