Keep our filled as we use the camper in the winter, even at home. When one tank gets empty, I get it filled it as fast as I can. Sometimes we have power outages at home. Although we have a generator, I prefer to run the generator and run a wire to the television, the refrigerator and freezer,the internet modem, and a light. (we have a fire place for heat in the house).
But we are in the country, so we are on a well, and the entire house is electric. It's kind of nice knowing there is always propane for the camper. We can always fix meals on the gas stove or oven if we need to. Also we can heat water on the trailer stove if the power is out long enough. It's just nice having that propane source.
Longest we've been out of power at the house was about 24 hours. We switched wires all over the house from the generator to run various appliances. But it was sweet using the camper to fix meals.
Filled or not... won't matter over the winter months.