I have no doubt a country "could" acquire and hold a prescriptive easement ..IF it met all the requisite conditions, same as other folks ..I. M not an attorney nor in TX but Judon Fambrough at Texas A& M is both and has a paper on topic on line .
At least as he describes the requisite conditions ...grading the roadway from time to time is not even close to meeting the requirements in TX law. But you forgot to mention that in first post and OT begins to muddy the waters.
But you'd be smart to get some seasoned legal TX input.
BTW ..IF the prior owner granted permission for use or grading it may be fatal to County view, Ditto if the prior owner made personal use of the graded roadway, it may be fatal to county view, and last but not least, the law may bar or frown up creation of prescriptive easement to purely recreational or unimproved lands
BTW just what kind of warranty as to title did the prior owner give you ? If the seller is on the hook as to title, it sure might help if seller has clear memory/records as to grant of permission and his use of roadway as well.
I live down a drive which is not where the roadway is supposed to be and there are all kinds of loose ends as to permissions dating from 1930s and missing paperwork ...and NJ has some similar issues as to not recognizing an easement of necessity to unimproved lands ...OUCH...none of this matters..what does matter is the TX law and facts ..and aside from bully power...the county is way short on facts at least as advanced by commissioner
I could not find a working link to that TX AG opinion..no clue what it reports to say. But I did find a an AG opinion on country expenditures for private roads