TexasCHLforum.com

Go to PC 30.05 and PC 46.02 & PC 46.03 for carrying without a license.
I'm not a lawyer, but the way I read it is that if you aren't in your home or vehicle, or between the two, you cannot carry a concealed handgun (thus the need to have a license to carry one anyplace else) unless you have specific permission by the owner of the property.

As far as laying it on your seat in your car or truck with a towel over it, IMHO that is not concealed. I have not been stopped very often for traffic violations, but one thing that I have been told by a couple of LEO friends is "Do NOT do anything other than sit with your hands on the steering wheel until we get to your window. If we see you moving around in your car we get very nervous and very suspicious."