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;