Sorry I'm a bit scatter brained and pressed for time lately so earlier I just tried to get as much information out as quickly as I could.
Here's the reference for bringing a firearm onto a correctional facility. Because of the dangerous possibility of an offender taking a firearm and using it, we will not even allow a uniformed, on-duty peace officer to bring his weapons or ammo inside the perimeter, and have secure storage boxes outside the perimeter for official use. We actually had an officer argue with our perimeter bosses about it one time and even though he had official business to conduct inside, we turned him away because he refused to relinquish his weapon. We were unofficially commended for our courage in the face of perceived authority.
TEX PE. CODE ANN. § 38.11 : Texas Statutes - Section 38.11: PROHIBITED SUBSTANCES AND ITEMS IN ADULT OR JUVENILE CORRECTIONAL OR DETENTION FACILITY OR ON PROPERTY OF TEXAS DEPARTMENT OF CRIMINAL JUSTICE OR TEXAS YOUTH COMMISSION
Text of subsection as amended by Acts 2005, 79th Leg., R.S., Ch. 1092 Sec. 1
(a) A person commits an offense if the person provides:
(1) an alcoholic beverage, controlled substance, or dangerous drug to an inmate of a correctional facility, except on the prescription of a physician or practitioner, as defined in Section 551.003, Occupations Code;
(2) a deadly weapon to an inmate of a correctional facility;
(3) a cellular telephone or other wireless communications device or a component of one of those devices, cigarette, tobacco product, or money to an inmate of a correctional facility operated by or under contract with the Texas Department of Criminal Justice;
(4) a cellular telephone or money to a person confined in a local jail regulated by the Commission on Jail Standards; or
(5) a cigarette or tobacco product to a person confined in a local jail regulated by the Commission on Jail Standards and in providing the cigarette or tobacco product the person violates a rule or regulation adopted by the sheriff or jail administrator that:
(A) prohibits the possession of a cigarette or tobacco product by an inmate confined in the jail; or
(B) places restrictions on:
(i) the possession of a cigarette or tobacco product by an inmate confined in the jail; or
(ii) the manner in which a cigarette or tobacco product may be provided to an inmate confined in the jail.
(b) A person commits an offense if the person takes an alcoholic beverage, controlled substance, or dangerous drug into a correctional facility or a secure correctional facility or secure detention facility for juveniles, except for delivery to a facility warehouse, pharmacy, or physician.
(c) A person commits an offense if the person takes a controlled substance or dangerous drug on property owned, used, or controlled by the Texas Department of Criminal Justice, the Texas Youth Commission, or a secure correctional facility or secure detention facility for juveniles, except for delivery to a warehouse, pharmacy, or physician on property owned, used, or controlled by the department, the commission, or the facility.
(d) A person commits an offense if the person:
(1) possesses a controlled substance or dangerous drug while:
(A) on property owned, used, or controlled by the Texas Department of Criminal Justice, the Texas Youth Commission, or a secure correctional facility or secure detention facility for juveniles; or
(B) in a correctional facility or a secure correctional facility or secure detention facility for juveniles; or
(2) possesses a deadly weapon while in a correctional facility or in a secure correctional facility or secure detention facility for juveniles.
....
(g) An offense under this section is a felony of the third degree.
I understand that you aren't going into a secure area, but I wanted to provide the precedent so you got an idea of the general outlook on guns in a correctional setting. Knowing how seriously they look on guns inside the perimeter should give you an idea of how they feel about them outside the perimeter. Notice also that when referring to drugs the law makes repeated mention of "property owned, used, or controlled by [correctional agency]". The parking lot of a correctional facility is regulated to one degree or another. Typically due to the state-wide staffing crisis we don't have the manpower to put someone at the highway gate, but every unit I've ever been to has a guardhouse and locking gate at the entrance to the parking lot. At the entrance to every unit parking lot is a large yellow sign explaining that by proceeding past said sign you agree to submit to search. TDCJ takes security very seriously even outside the secure perimeter. Anything on state prison property is controlled.
While I can't reference a law on the subject of public access, it's one of those things where (from my understanding) if you don't have business there,
leave. Our Mobile Patrol unit will immediately investigate any vehicle in our parking lot that isn't identified as staff or a visitor on a visitation day, and if they have no business there he will tell them to leave. If they don't, the highest ranking supervisor present (usually a Lieutenant at night and the Warden during the day) will tell them to leave. If they refuse the local PD are called because someone with no official business on the premises is a security risk. There is a pretty wide berth on that. Anything that is deemed a security risk is dealt with swiftly and without compromise. I'm honestly not sure if there is law behind that or if it is just a combination of common sense and agency policy.
I find that much of what we are taught is factual, it is simply that so many officers are...shall we say
entry-level, that the laws are not taught because they would be immediately forgotten. These are typically the kind of...
employees that need refresher courses on how to work handcuffs...and then they still get it wrong. The average LTC holder is a genius by comparison to the average TDC officer. Obviously there are exceptions to both, but you get what I mean, right? I wasn't taught the laws surrounding this stuff because the average IQ isn't high enough to need a "1" at the start. As such, I try to teach what will result in the fewest potential problems, even if it isn't supported.
That's another thing you should know about TDC officers. We are used to dealing with offenders all day: uneducated thugs with attitude problems and a severe case of entitlement mentality. As a general rule, "I'm right, you're wrong, shut up, go away" is the mindset of an officer because let's face it, most of the time when dealing with an offender
it's true. Unfortunately, this mentality doesn't like to go away. We tend to apply it subconsciously to every interaction
especially if in uniform. If you get in an argument with an on-duty CO, you're going to lose because he doesn't believe in defeat. When that happens, you will be escorted from the premises - by local PD or the sheriff if necessary. Not trying to say that's right, just telling it like it is.
Hope this was more helpful. Not trying to be a jerk here, just trying to prepare you for the reality of what you may find when you go.
By the way, as you've noticed I use TDC and TDCJ interchangeably so it doesn't matter to me, but the official name is now TDCJ (Texas Department of Criminal Justice), not TDC (Texas Department of Corrections). It was changed when the state restructured and included parole offices and a few other agencies with the prison system.

Never bring a knife to a gun fight.
Carry gun: Springfield XD Tactical .45