Regular home use refrigerators don't do well in cold or hot areas, but since you're only running it in warm months it shouldn't be a big issue other than the extra electricity it will use in hot weather.
The t-stat won't work correctly in freezing temps, so the compressor will short cycle. This can mess up the defrost timer cycle, but what happens most often is the refrigerated foods freeze. The refrigerant oil can gel and could lead to compressor failure, but it's rare. After your winter shutdown , don't plug it in until the temp has been steadily above 50° for a day or two.
Tommy