As far as liability/DOT weights go, its registered GVW of truck (13K) + registered GVW of trailer (whatever it is) = GCVW, and if that figure is over 26K you need the CDL.
If it is a short trip, check with you local DMV website. If you are going to be crossing state lines, follow federal DOT regs as well.
Actually this might be the only time I disagree with your reading of regs, from DOT book.
A commercial driver’s license (CDL) is required for anyone driving any of the
following sizes or types of vehicles.
A single vehicle with a Gross Vehicle Weight Rating (GVWR) of more
than 26,000 pounds.
A combination vehicle with a Gross Combined Weight Rating (GCWR) of
more than 26,000 pounds when the towed vehicle GVWR is over 10,000
A passenger vehicle has a seating capacity for 16 or more persons,
including the driver.
A vehicle transports hazardous material in a quantity requiring a placard.
using his F250 it's GVWR is 10k or less, so as long has he has it registered for 13k or less and he weighs 26k or less he does not need a CDL.
Howerver his F350 would require a CDL.
In Iowa as long as it's farm related (including hauling junk) and your own truck, it is excluded from CDL liscensing requirements, even to drive a semi.