remember the cdl requirements start at 26,000 unless you are exempt. (agriculture, etc.)
be sure to check state laws, and perhaps the cmvsa website for exemptions. even if your truck does not have air brakes, but weighs in over 26,000, you MAY have to have a cdl.
i can't see anybody hassling the owner of a classic truck, but i'm sure they are out there.
there ought to be an exemption for classic vehicles.