This question is often asked and even more often debated. Bottom line, a CDL shows that you are somewhat competent and have demonstrated knowledge of heavy vehicle operation and systems if you obtain the endorsements like air brakes.
That being said, many (unknowing but trying to be helpful) people will insist that it is a "commercial vehicle and you need a CDL due to federal laws."
-WRONG!!!
Once it is tagged and insured by a state as an antique or collectible vehicle, it is NO LONGER a commercial vehicle. Period. It is now a privately owned antique or collectible vehicle that may happen to weigh in excess of 26,001 lbs. And many states do not require a CDL to operate an antique or collectible vehicle even if it is in excess of 26,001 and has air brakes.
You need to check with your individual state, but you need to make sure you are speaking with someone who is knowledgeable of the motor vehicle codes of that state. If you walk into the local branch office of the DMV, the clerk behind the counter may or may not know anything about it- more than likely if you say the words "antique tractor trailer" they will probably go into vapor lock.
In Pennsylvania- a CDL is NOT needed to operate a vehicle weighing in excess of 26,001 lbs with air brakes that is tagged and insured as an antique vehicle and is not used within the definition of "Commerce."