The law allows you to transport a firearm without a license as long as the gun is not accessable when in the car. My understanding is, and I could be wrong, that you are not allowed to store the gun in your car. You can drink and carry but not be intoxicated
Good FAQ
http://www.texaschl.us/faq.htm#carrying
Bottom line is you are NOT allowed to carry while intoxacated. And, as the definition of carrying includes a firearm that you can reach without materialy changing your position in the car, (that has been ruled to include basicly anywhere with in reach,: Glove compartment, under the seat, purse or seat next to you, etc) you can get nailed quite easily. So in addition to the DWI, you get a carrying charge as well. Or what ever the actual charge would be.