Depending on the part of the country, most box turtles in the wild hibernate. In northern states they may hibernate for 6 months while in Florida and along the gulf coast they may only slow down during the cooler winter months and not enter a true hibernation state.
Here in South Carolina mine will dig in around mid October and re-appear late April. Hibernation is triggered by many cues such as decreasing daylight hours and lower temperatures. With mine it seems night temperatures are the main trigger. When it starts getting into the low 40's at night, they dig in. I think soil temps play a role as well. My 3-toeds are in a pen that gets allot more direct sunlight in the fall and the soil stays warmer. The 3-toeds typically dig in a few weeks later than the others in the shadier pens.
To prepare for hibernation, I make a mound of hay and leaves in the center of the pen. I arrange the hay so there are caves and pile the leaves on top of that. When the turtles stop appearing to bask in the morning, I cover the pile with a tarp to keep it from getting too wet during our frequent winter rains.
While some feel that in a large pen with plants and If you have your colony in a large, naturalistic outdoor habitat, with vegetation, sun & shade, burrowing substrata, a little pond, hide logs, etc., the turtles should be able to stay outdoors all year. They will not hibernate above 50ºF. But even just cooling down for awhile is natural and probably beneficial for them. As temperatures cool, outdoor turtles will naturally stop eating.
If they are housed indoors, and don't have the opportunity to react to the changing weather, you must stop feeding them at least 2-3 weeks prior to hibernation. Then they will need a good soak in tepid water to encourage elimination. You want a bunch of partially digested food in the intestinal tract. Box turtles hibernate at temperatures between the freezing point+ and about 50. They burrow to find safe temperatures if they live in cold regions, to maintain themselves between those temps.
If you want to use a refrigerator, maintain the temperature at 39-42º. I use plastic sweater boxes with moist sphagnum moss. I have a refrigerator that is used only for hibernating turtles. I tape a pencil in the door seal to prevent it from completely sealing up, which might prevent the minimal O2 - CO2 gas exchange needed. I also check on them each week or so. I even take them out and soak them every 2 weeks or so. I have never lost any turtle hibernating in the fridge.
Don't hibernate any turtle until you have had it for at least a year and are certain it is healthy. Don't hibernate any turtle that has been ill during the preceding year. Don't hibernate a "picky eater" because it is likely to be lacking some nutritional element. A turtle that is compromised in any way would not be a good candidate for hibernation. There is quite a bit to learn about hibernation before you try it. You really have to balance the benefits against the dangers, and take precautions. I don't think that anyone should feel "forced" to hibernate a turtle, at least not until they have studied up on the idea and are comfortable with it.