Found a new posting... it was lowered to 15 MPH for the beach in general for all texas beaches, and also 15 MPH for county roads alongside the beaches..
Dune-driving is illegal still... looks like some sites rate the beach as a 3 of 10 for how hard it is to tackle for offroading... and most also say it's not too hard for a 4x2 to handle assuming you have clearance (we do!). Since you can't do the dunes, it's mostly scenic driving supposedly.
Also, while some parts of the gulf coast beach is privately owned, the public has access to all of it through a long-standing public access easement... although that may not mean you can drive on it, you can at least walk it all.
Hmmm, maybe I'll take my X down to Galveston or Corpus this summer to goof around.