TexasCHLforum.com

Penal Code 46.035(3) defines premises:

(3) "Premises" means a building or a portion of a building. The term does not include any public or private driveway, street, sidewalk or walkway, parking lot, parking garage, or other parking area.

You can thank Charles for that wording.
46.03(3) states

(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;

Therefore, by law (Charles, correct me if I'm wrong), the premises of a court or offices of that court would be the physical location where that court and/or offices resides within the building, not the entire building.

SB 273, passed in the most recent session, signed by Governor Abbott on Jun 16th and effective 9/1/2015, amends the Government Code 411 to provide for civil penalties for any government agency that improperly posts a government building and provides that a citizen can file a complaint with the State Attorney General's office, which will investigate to see if a violation has occurred, after the citizen has provided written notice to the agency, if the agency does not cure the violation within 3 business days.

Government Code 411.209(d)

(d) A citizen of this state or a person licensed to carry a
concealed handgun under this subchapter may file a complaint with
the attorney general that a state agency or political subdivision
is in violation of Subsection (a) if the citizen or person provides
the agency or subdivision a written notice that describes the
violation and specific location of the sign found to be in violation
and the agency or subdivision does not cure the violation before the
end of the third business day after the date of receiving the
written notice. A complaint filed under this subsection must
include evidence of the violation and a copy of the written notice.

So the OP, who asked his question in 2011, may, after 9/1/2015, notify the Cotton Belt Building that they are in violation of the statutes, give them 3 days to rectify and state that he will formally complain to the Governor if they do not comply.

Disclaimer: I am not a lawyer. This is my interpretation of the statutes. Charles can correct me if I'm wrong. Before walking into such a building, I would first obtain a valid legal opinion (which you can ask your representative to obtain from the State Attorney General's office at no charge).