Texas doesn't ban open carry of handguns; Texas bans carry, period, then gives some exceptions.
One exception is carrying a concealed handgun with a concealed handgun license; another is being in a motor vehicle you own or control, so long as the handgun is concealed. Those are the only two exceptions where being open or concealed matters.
For other exceptions, like being on your own property, you can carry openly or concealed, loaded or unloaded, because the ban on carrying no longer applies.
Texas Penal Code 46.02 makes it an offense to carry a handgun on or about your person. Then in Sec. 46.15. NONAPPLICABILITY:
(b) Section 46.02 does not apply to a person who:
(3) is engaging in lawful hunting, fishing, or other sporting activity on the immediate premises where the activity is conducted, or is en route between the premises and the actor's residence or motor vehicle, if the weapon is a type commonly used in the activity;