WARN winches have their serial number either laser etched or stamped. In most cases, the serial number is located on the gear housing side of the winch.
It is important to know that many of the warn electric motors that drive the winch gear train also have serial numbers. The motor information helps identify the motor but not the specifics about the particular warn winch it is mounted on.
This is an example of the data tag on a WARN winch electric motor. The M space is the WARN part number for the motor.