Here's the skinny on the peaceable travel in TX. NM mirrors this.
________Peaceable journey law summary:
This section last updated Aug 21, 2000
There is a "traveling" exemption in the law for non-CHL holders -- it is no longer a "defense to prosecution", but instead renders the prohibition "not applicable" (see PC 46.15 of the Penal Code) However, "traveling" is still defined by case law, and varies between jurisdictions. The alleged rule about "crossing two county lines" is case law, and not binding. I wouldn't advise anyone to depend on it.
Summary:
Basically, you have to be directly enroute between two distant points. It also must be a "non-routine" trip -- commuting to work doesn't count. Someone from out of state would almost certainly be traveling, but only while actually in transit. Once you get to your destination in Texas, you can't carry it around in your car and claim to be traveling -- at least not until you embark on your return trip home.
Also, this prohibition only applies to handguns. Long guns are not prohibited by this law, although there are some municipalities that have enacted local regulations (which are in violation of state law, but that's another matter).