Your trailer lights are submerged, too & use the same 12 volt power supply ....
As long as the unit is sealed (I imagine it would be, even if designed for trailers that aren't submerged, they still have to stand up to rain and puddles) you shouldn't have any trouble.
If you're worried about it, put a tandem switch at the bumper near your license plate so that you can just flip a switch on & off to cut power to the trailer.