TexasCHLforum.com

I'm not a lawyer. The short version is you can carry in your car if it's concealed and you're not a criminal.

Here's the actual law.
Sec. 46.02. UNLAWFUL CARRYING WEAPONS. (a) A person commits an offense if the person intentionally, knowingly, or recklessly carries on or about his or her person a handgun, illegal knife, or club if the person is not:
(1) on the person's own premises or premises under the person's control; or
(2) inside of or directly en route to a motor vehicle that is owned by the person or under the person's control.

(a-1) A person commits an offense if the person intentionally, knowingly, or recklessly carries on or about his or her person a handgun in a motor vehicle that is owned by the person or under the person's control at any time in which:
(1) the handgun is in plain view; or
(2) the person is:
(A) engaged in criminal activity, other than a Class C misdemeanor that is a violation of a law or ordinance regulating traffic;
(B) prohibited by law from possessing a firearm; or
(C) a member of a criminal street gang, as defined by Section 71.01.

(a-2) For purposes of this section, "premises" includes real property and a recreational vehicle that is being used as living quarters, regardless of whether that use is temporary or permanent. In this subsection, "recreational vehicle" means a motor vehicle primarily designed as temporary living quarters or a vehicle that contains temporary living quarters and is designed to be towed by a motor vehicle. The term includes a travel trailer, camping trailer, truck camper, motor home, and horse trailer with living quarters.

(b) Except as provided by Subsection (c), an offense under this section is a Class A misdemeanor.

(c) An offense under this section is a felony of the third degree if the offense is committed on any premises licensed or issued a permit by this state for the sale of alcoholic beverages.