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The law states: (Please excuse the lack of formatting)

Note: This does not apply to peace officers, including commissioned peace officers of a recognized state, or special investigators under Article 2.122, Code of Criminal Procedure, and neither section prohibits a peace officer or special investigator from carrying a weapon in this state, including in an establishment in this state serving the public, regardless of whether the peace officer or special investigator is engaged in the actual discharge of the officer's or investigator's duties while carrying the weapon;

and

Note: This does not apply to an honorably retired peace officer or federal criminal investigator who holds a certificate of proficiency issued under Section 1701.357, Occupations Code, and is carrying a photo identification that (A) verifies that the officer honorably retired after not less than 20 years of service as a commissioned officer; and (B) is issued by the agency from which the peace officer retired or, for a federal criminal investigator, by a state law enforcement agency.

I was made aware of this information by Excalibur.

CHAPTER 46. WEAPONS

§ 46.03. PLACES WEAPONS PROHIBITED.
(a) A person commits an offense if the person intentionally, knowingly, or recklessly possesses or goes with a firearm, illegal knife, club, or prohibited weapon listed in Section 46.05(a):
(1) on the physical premises of a school or educational institution, any grounds or building on which an activity sponsored by a school or educational institution is being conducted, or a passenger transportation vehicle of a school or educational institution, whether the school or educational institution is public or private, unless pursuant to written regulations or written authorization of the institution;
(2) on the premises of a polling place on the day of an election or while early voting is in progress;
(3) on the premises of any government court or offices utilized by the court, unless pursuant to written regulations or written authorization of the court;
(4) on the premises of a racetrack;
(5) in or into a secured area of an airport; or
(6) within 1,000 feet of premises the location of which is designated by the Texas Department of Criminal Justice as a place of execution under Article 43.19, Code of Criminal Procedure, on a day that a sentence of death is set to be imposed on the designated premises and the person received notice that:
(A) going within 1,000 feet of the premises with a weapon listed under this subsection was prohibited; or
(B) possessing a weapon listed under this subsection within 1,000 feet of the premises was prohibited.
(b) It is a defense to prosecution under Subsections (a)(1)-(4) that the actor possessed a firearm while in the actual discharge of his official duties as a member of the armed forces or national guard or a guard employed by a penal institution, or an officer of the court.
(c) In this section:
(1) "Premises" has the meaning assigned by Section 46.035.
(2) "Secured area" means an area of an airport terminal building to which access is controlled by the inspection of persons and property under federal law.
(d) It is a defense to prosecution under Subsection (a)(5) that the actor possessed a firearm or club while traveling to or from the actor's place of assignment or in the actual discharge of duties as:
(1) a member of the armed forces or national guard;
(2) a guard employed by a penal institution; or
(3) a security officer commissioned by the Texas Board of Private Investigators and Private Security Agencies if:
(A) the actor is wearing a distinctive uniform; and
(B) the firearm or club is in plain view; or
(4) Deleted by Acts 1995, 74th Leg., ch. 318, § 17, eff. Sept. 1, 1995.
(5) a security officer who holds a personal protection authorization under the Private Investigators and Private Security Agencies Act (Article 4413(29bb), Vernon's Texas Civil Statutes).
(e) It is a defense to prosecution under Subsection (a)(5) that the actor checked all firearms as baggage in accordance with federal or state law or regulations before entering a secured area.
(f) It is not a defense to prosecution under this section that the actor possessed a handgun and was licensed to carry a concealed handgun under Subchapter H, Chapter 411, Government Code.
(g) An offense under this section is a third degree felony.
(h) It is a defense to prosecution under Subsection (a)(4) that the actor possessed a firearm or club while traveling to or from the actor's place of assignment or in the actual discharge of duties as a security officer commissioned by the Texas Board of Private Investigators and Private Security Agencies, if:
(1) the actor is wearing a distinctive uniform; and
(2) the firearm or club is in plain view.
(i) It is an exception to the application of Subsection (a)(6) that the actor possessed a firearm or club:
(1) while in a vehicle being driven on a public road; or
(2) at the actor's residence or place of employment.