There is a basic reality that is being missed in several posts on this issue. No matter what energy is being used--gasoline, electricity, wood, coal (or even nuclear)--it takes MORE energy to GET a thing moving, cooling, heating, than it does to KEEP a thing moving, cooling, or heating. If you doubt this basic scientific principle--albeit, stated in layman's terms--just hop on a bicycle, and start peddling. You will quickly find that it is far harder to GET it moving, than it is to KEEP it moving. The same is true for an automobile, and that is why highway travel mileage is so much higher than city travel mileage.
The same principle applies to refrigeration, which includes refrigerators and freezers, as well as air-conditioners. It takes far more energy, that is electricity, to cool something warm, than it does to KEEP cool something that is already cool. I learned this as a small child, from my father, who was a commercial and industrial mechanical engineer, with a specialty in air-conditioning and heating, so it does not take a very experienced adult, with years of education, to understand the basics.
YES, if you turn off a refrigerator you are using less--indeed, NO--electricity, while it is off, but the same thing holds true for an automobile. Next time you are going somewhere, simply turn the ignition key off, and you will be surprised how much gas you save. Of course you will not get very far, but... That is no less true for refrigerators. Besides using MORE electricity to GET the fridge cool again, you will lose much of the health benefits of keeping food much cooler than room temperature. As stated on the FDA Website, "When it comes to protecting yourself and your family from foodborne [sic] illness, one of your most effective tools is the kitchen refrigerator. In fact, at room temperature, the numbers of bacteria that cause foodborne [sic] sickness can double every 20 minutes! Chilling foods to proper temperatures is one of the best ways to slow the growth of these bacteria."
If you are contemplating turning your refrigerator off once or twice a day, for a couple of hours, or all night, and you are doing so because a power company suggested it, consider the source. Do you really think that a power company is concerned about saving you money, or is it perhaps that it wishes to reduce its power demands?