[NiHaoMike]

There is a minimum, but the reason you stated is not why. The problem is that with a typical capillary tube refrigerator, the high side must have enough pressure for it to work. At low temperatures, there won't be enough pressure. There might also be problems with the compressor oil being too thick and not allowing it to startup correctly.

To solve these problems, install a hard start kit and a compressor heater band with a thermostat. Then replace the fixed speed fan with a variable speed one (those made for PC cooling should work great) that adjusts speed depending on the temperature of the condenser.