Ok, lets look at the known facts.<ul>The lights came on by themselves while the truck was sitting parked.
They stay on with the ignition switch OFF and the fuse pulled (i.e. no normal source of battery power to the lamps.)
The D's been driven in heavy snow conditions recently.
He left the tow harness adapter plugged in and the tow harness shares electrical connections with the rear lights to power the trailer lamps.[/list]So?
While it's always possible it could be something else, the evidence is highly suggestive that a short has developed in the shared wiring between the tow harness and the rear lights that's allowing battery voltage to find it's way to the backup lights from a "powered" lead in the towing harness (possible due to build up of wet snow somewhere in the wires between the tow harness and the lights??) Other than the shared leads from the rear lights (and we already know pulling the fuse for the lights doesn't kill power to the backup lamps) the only other source of power in the tow harness comes from the trailer fuse in the PDC. I'd suggest pulling that fuse and see if that kills the power to the lights.
If so, then your short is gonna be in the tow harness wiring and, as long as you don't need to tow anything until then, you can just leave that particular fuse out until the weather warms up so you can crawl under your D and locate/fix the problem.
If pulling the trailer fuse doesn't help, then you've got a short to a power source somewhere else that's likely gonna be a PITA to track down!