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(8) "Institution of higher education" means any public technical institute, public junior college, public senior college or university, medical or dental unit, public state college, or other agency of higher education as defined in this section.

Sec. 411.2031. CARRYING OF HANDGUNS BY LICENSE HOLDERS ON
CAMPUSES. (a) For purposes of this section:
(1) "Campus" means all land and buildings owned or leased by an institution of higher education.
(2) "Institution of higher education" has the meaning assigned by Section 61.003, Education Code.(3) "Premises" has the meaning assigned by Section 46.035, Penal Code.
(b) Except as otherwise provided by this section, a license holder may carry a concealed handgun on or about the license holder's person while the license holder is on the campus of an institution of higher education in this state.
(c) Except as provided by Subsection (d), an institution of higher education in this state may not adopt any rule, regulation, or other provision prohibiting license holders from carrying handguns on the campus of the institution.
(d) An institution of higher education in this state may establish rules, regulations, or other provisions concerning the storage of handguns in dormitories that are owned or operated by the institution and located on the campus of the institution.
(e) This section does not permit a license holder to carry a concealed handgun on or about the premises of a hospital maintained or operated by an institution of higher education. In this subsection, "hospital" has the meaning assigned by Section 241.003, Health and Safety Code.
(f) This section does not permit a license holder to carry a concealed handgun on the premises of a preschool, elementary school, or secondary school that is located on the campus of an institution of higher education if the institution gives effective notice under Section 30.06, Penal Code.

The pivotal part is what "institution of higher education" includes. According to Education Code §61.003:

(8) "Institution of higher education" means any public technical institute, public junior college, public senior college or university, medical or dental unit, public state college, or other agency of higher education as defined in this section.

Note that "other agency of higher education" isn't just a catch-all term--it is defined as specific institutions. I think that it would still be illegal to carry on the premises of a private college, since the exception added to the penal code only applies to "an institution of higher education":

(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:
(A) pursuant to written regulations or written
authorization of the institution; or
(B) the person possesses or goes with a concealed
handgun that the person is licensed to carry under Subchapter H,
Chapter 411, Government Code, and no other weapon to which this
section applies, on the physical premises of an institution of
higher education or in a passenger transportation vehicle of the
institution; "

(15) "Private or independent institution of higher education" includes only a private or independent college or university that is:(A) organized under the Texas Non-Profit Corporation Act (Article 1396-1.01 et seq., Vernon's Texas Civil Statutes);(B) exempt from taxation under Article VIII, Section 2, of the Texas Constitution and Section 501(c)(3) of the Internal Revenue Code of 1986 (26 U.S.C. Section 501); and(C) accredited by:(i) the Commission on Colleges of the Southern Association of Colleges and Schools;(ii) the Liaison Committee on Medical Education; or(iii) the American Bar Association.