You'll be fine. You're only looking at 2-4 hours for the low which will be right at maybe freezing and that is for the outside air. With your trailer in your pole barn, there is a bit of insulation from the low so very doubtful it will even get to freezing temps inside the barn but if it did, again, only a few hours max at 32. If you're still concerned, do as suggested and set your thermostat at its lowest setting to have the heat come on.
You need to be more concerned when there is a hard freeze.
I love me some land yachting