You should run antifreeze through it if the trailer is going to see freezing temperatures. On-demand water heaters are built similar to a car radiator but acts in reverse. There are many tubing bends and flat sections of tubing that can hold water.
I have a portable outdoor on-demand water heater I have used when tent camping, with my pop up and when bathing the dog outdoors at home. After sitting for awhile thinking it was drained I picked it up to move it and water dribbled out. After using it I always bring it inside at home to store it. If I were to leave it outside in the shed for winter, I would definitely put antifreeze through it.