I won't get very deep into this, because over time, this thread will surely end up filled with loads of false information due to people believing whatever they want to believe in order to justify carrying a weapon in their truck.
First off, you have to have a license to carry a concealed handgun,
and any State you happen to be in will either have to accept the license you have, or you will have to be licensed in their State (otherwise, you are illegally carrying the gun in their State)
Second, is company policy and insurance.
If the company you work for, or are leased to, doesn't allow guns in trucks, you can't do it without the risk of being immediately terminated if caught.
Third, shipper/receiver rules must be obeyed.
This is the one that everyone seems to forget about or somehow try to ignore when they argue this topic. If the customer has a policy that doesn't allow firearms on their property, you cannot enter their property with the gun in your possession (in your truck). For me, this debate pretty much ends here because the majority of businesses DO NOT allow firearms on their property.
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Now, if you do carry a firearm in your truck, with or without a permit (and I am not endorsing carrying a gun in your truck), be smart and keep this information to yourself. Don't mention it to anybody, don't show it to anybody, ever. Pretend it doesn't exist unless an unfortunate situation develops where you need it.