Normal operation is when the fridge side needs to be cooled the compressor will run. It cools the freezer directly (making it much colder) and cools the fridge indirectly to keep things from freezing. The temperature sensor is usually triggered by the fridge.

The problem is, the garage is so cold it's cooling the fridge side to below the temp to start the compressor, but it's not cold enough to keep your freezer at zero to freeze your non-water stuff. The fridge thinks it's cold enough so the compressor never kicks on.

Whatever cheap stupid solution works. Those handwarmer packet things aren't a bad idea. I had an old incandescent worklight that I hooked up to a timer and hung it in the fridge and it worked like a charm. Basically whatever will warm the fridge side juuuust enough to (periodically) get the compressor to fire up.

Source for all the above: dad's a commercial refrigeration guy.