Here's what I gather.
Many freezers are controlled by not only sensing the internal temperature but also sensing the difference with the exterior temperature, and they may be designed to shut down when the exterior temperature drops to near the desired internal temperature.
It is not a matter of refrigeration simply in general not working in a cold environment. Truck refrigeration units work in all temperatures. But home appliances are never engineered to be as robust or as flexible as commercial equipment. Why should they, when almost all of their products will be used inside as intended.
Figure that the usual home freezer may very well have difficulty in a room that's below freezing. It might be damage to the unit. It might be that it simply stops working, and your food thaws. So what to do?
I don't think turning the freezer off during a cold spell will work. The damage maybe done before it gets that cold. It could be too cold to run but not cold enough for the food. And you'd have to monitor the temperature independently. A pain.
You could heat the garage, but there are also accessory heaters for refrigerators that keep the local temperature at the coils high enough to keep it running.
Frigidaire - Garage Refrigerator Heater Kit
It should work with a freezer, since a refrigerator is just a freezer with a duct to steal cold for the other half. Ask Frigidaire about it and about the warnings about the age of the unit (which side of 2001) and the computer control situation. And it may be limited to top freezer refrigerators.
Obviously, the best would be a heater designed by the freezer maker for that model. If nothing is made that will work installed in the freezer, the alternative might be to build in around the freezer so it can be heated by a small space heater on a thermostat.
I personally would just put the thing in the cellar and be done with it. Or I wouldn't spend too much on the freezer and put it in the garage, but put in a freezer alarm. They're very cheap. If you found out it got too cold for the freezer to run, you could say "I told you so" and haul it to the cellar.