Refrigerator freezes
If your refrigerator is in an unheated part of your house and that area regularly reaches temperatures below freezing, your refrigerator will eventually freeze.  Good fridges are certainly insulated well but no amount of insulation will prevent temperature change over time, particularly if you're opening and closing the fridge. Refrigerators only cool. They don't have heating elements.

The only possible way to keep your fridge from freezing during the winter is to store it somewhere that stays above freezing or work out some sort of hack where you hook a heating element (say a heat lamp) up to a thermometer and whenever it hits below 33F (1C), it turns on for a short period of time to bump the temperature back up again.

When we were brewing beer during the winter we occasionally had to do something like this as our fermenting fridge needed to be kept at 70F (21C). We had a special setup, though, which allowed one compartment to have the heat lamp and a fan to blow the warm air into the beer compartment. This prevented hot spots, which would be really bad for you in the case of perishable foods.