Your home state's weapons carry laws have no effect on the state that you travel to. For instance, if you travel to Wyoming you can open carry there and in your car regardless of Arkansas restrictions or Arkansas CHL. You have to obey the laws of the state that you are physically located in.
Some states require a permit just to possess a handgun. If you travel THROUGH that state, you may transport your handgun in accordance with FOPA, but if you travel TO that state, and it is your destination, then you might be in illegal possession of a handgun according to that state's laws.
Most states "allow" open carry by means of there are no laws making it illegal.