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More specifically related to campus' and students:

GC §411.2032. TRANSPORTATION AND STORAGE OF FIREARMS AND
AMMUNITION BY LICENSE HOLDERS IN PRIVATE VEHICLES ON CERTAIN
CAMPUSES. (a) For purposes of this section:
(1) “Campus” means all land and buildings owned or leased by an institution of
higher education or private or independent institution of higher education.
(2) “Institution of higher education” and “private or independent institution of
higher education” have the meanings assigned by Section 61.003, Education
Code.
(b) An institution of higher education or private or independent institution of
higher education in this state may not adopt or enforce any rule, regulation,
or other provision or take any other action, including posting notice under
Section 30.06, Penal Code, prohibiting or placing restrictions on the storage or
transportation of a firearm or ammunition in a locked, privately owned or leased
motor vehicle by a person, including a student enrolled at that institution, who
holds a license to carry a concealed handgun under this subchapter and lawfully
possesses the firearm or ammunition:
(1) on a street or driveway located on the campus of the institution; or
(2) in a parking lot, parking garage, or other parking area located on the
campus of the institution.

If the student or university employee did not have a CHL, the university could prohibit vehicles with firearms by policy. The policy would only apply to students or employees of course.