For Oklahoma:

5. May I transport a firearm in my motor vehicle?

Answer: Under Oklahoma law, the general rule is that any person, except a convicted felon, may transport in a motor vehicle a firearm open and unloaded at any time. “Open” means the gun is in plain view or in a case designed for carrying firearms provided the case is wholly or partially visible.

6. What should I do if I encounter a law enforcement officer while carrying a gun?

Answer: State law requires any person who is carrying a handgun pursuant to a handgun license to immediately notify a law enforcement officer that he/she is carrying a firearm when the licensee comes into contact with the officer during any arrest, detainment or routine traffic stop.

http://www.okc.gov/okcpd/about/newsOKFirearms.html

TX-
The General Firearms Laws of The State of Texas:

In Texas, it is generally illegal to carry a handgun outside of a person’s own premises. However, a person may carry, either open or concealed, in a non-threatening or alarming manner, a shotgun or rifle.


https://www.texaslawshield.com/portal/texas-gun-law/

Thanks, Bob. That's very helpful.