Being from Florida (and familiar with the central florida topography) I would also say that freezing below the surface won't be a problem at all, even in most of northern Florida. The biggest problem you will have is moisture and water. Many wells in this area are only dug to about 40 feet-like mine. Thus, if you dig too deep water will be a huge problem. Also, a freezer, being mostly metal, may rust in a little over a year due to the sandy soil and the rainy season.
I personally wouldn't use a freezer but would try some other plastic container that is well sealed--to block out moisture, and oxygen absorbers. I must admit I am new to using oxygen absorbers so I can only assume they will work. Well now you got me thinking, now I am thinking about burying something in the yard just to test it out. The only way to know for sure is to try it.