There is a cool-down portion of the cycle that run after the thermostat opens. It may be that it's cold enough there that it cools off much quicker than it's designed for (after all, while the fan is running it's circulating outside air through the combustion-air side of the system as well as through the ducts within the trailer, so the heat exchanger probably cools off pretty quickly if it's 12F outside.)
Do you hear the thermostat click before the air turns cold? Does it do it at the end of every cycle or just sometimes, or do you only notice it if you're near one of the vents? Is this the original furnace with a pilot light or a replacement unit with spark ignition?
Il Carriaggio — 1975 Argosy 24 | Il Progetto — 1976 Argosy 28 Center Bath | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill