Cold Temperature Use - Refrigerator
Your owner's manual may specify a minimum external temperature for use, but, in practice, most refrigerators will continue to work normally until the outside temperatures approach the temperature inside the fridge. At that point, the thermostat will not come on, and the refrigerator will not cool, which may not be a problem since the temperature inside the fridge will stay close to the outside temperature; however, some fridge contents like beverages may be ruined if the temperature drops below freezing.
Cold Temperature Use - Freezer
While the refrigerator will continue to function, if the unit has an attached freezer, it may shut down when outside temperatures drop below 40 degrees Fahrenheit. Many refrigerator/freezer combos run off of a single thermostat located in the refrigerator section, so when the outside temperature drops below the refrigerator temperature, the thermostat does not come on and the freezer is not cooled. Test freezer function by placing a thermometer in among the food; it should read 0 degrees Fahrenheit.
Special Considerations for Outdoor Use
When using a refrigerator outdoors, ensure it is in a dry area and protected from the elements. Many garages and sheds have ground fault circuit interrupter (GFCI) systems to prevent shorts, but if the outlet switches off, the refrigerator won't run and the food may spoil. For the same reason, don't plug your refrigerator into an outlet that is controlled by a switch. Inspect the refrigerator at least daily to see that it's working properly.
As you might expect, a refrigerator will use less electricity when it's in a cold location. The flip side, of course, is that it will use far more energy if you leave it in an outdoor location during the summer in areas where outside temperatures are frequently high. If possible, use only your indoor refrigerator during hot periods, and save the outdoor refrigerator for fall, winter and spring use.