My Aunt has a seasonal cabin in NH. At the end of the fall we shut the water off and close down the cabin. Last year we had to gut and re-do the entire cabin due to a mold problem. Part of the problem had to do with water getting in the half basement and then mold forming, but even before that problem, it always had a mold issue. It's my understanding that it's probably the late fall early spring that causes the issue, but that is just speculation. I am interested in putting a de-humidifier in the cabin, to ensure that it stays fairly dry, but I'm concerned about the fact that it will soon get below freezing. Perhaps there is on that has a frost shutoff? or perhaps I can rig something that will turn it off when the temperature goes below a certain value. I'm looking for recommendations on how to tack this problem.
You are correct that dehumidifiers typically do not operate below freezing temperatures. In fact, many do not operate well if the temperature is below 65F. Certain high performance units are rated to operate down to temperatures a little above freezing.
If the goal is to suppress mold growth by maintaining indoor relative humidity below 55% during cold temperatures, then the obvious answer is that both a high performance dehumidifier and a heater are needed. Looking at the psychrometric chart for moist air, 56F air at 55% humidity has a dew point of 38F. With a high performance dehumidifier and a heater set to maintain an air temperature of at least 56F degrees, the RH of the air in the cabin could be maintained at or below 55%.
To dehumidify in the late fall/winter/early spring you don't need a dehumidifier at all. Simply adding heat will automatically lower the relative humidity. Of course, if you did not heavily insulate when rebuilding the cabin, this will be expensive to do.
You could get cute and use a humidistat to control the heater rather than a thermostat, but you can also simply run a small heater full time.