You could use a wood or coal fired steam engine to drive the compressor of a freezer - like
Doc Brown did in Back to the Future 2 (or was it 3?). OK, I know it was just a movie but it
seems to me that it could be done.
Where’s Runner Pat when you need him?
I assume it is a spam bot. I reported it as a possible spam. We will see.
Right, hence my oblique reference–RP is usually first on the scene.
I think I’ll start saying I “Runnerpatted” spambots. We can always use more esoteric verbs.
I had a funny feeling there was a reference there, but I was being too thick to grasp it 
Paper (PDF) on zeolite based zorption refrigerator:
http://fc.uni.edu.pe/mhorn/ISES2003%20(solar%20refrigeration).pdf
You heat the zeolite (solar can work) which drives out the water. Then cool it and it will absorb water vapor creating enough vacuum to cool water to ice via evaporation. I recall seeing one design which had the zeolite in large black roof mounted pipes, but I couldn’t find that paper.
Thing is, you probably won’t have permanent loss of electricity. Instead a more likely scenario is a reversion to Third World electrification–you get electricity a couple of hours a day on a random pattern.
So the real solution is to start making ice the minute you get electricity on, and always keep your freezer almost full of ice. The ice will keep your freezer cold even if you lose power for several days.
Also you might want to look into trying to add extra insulation to your freezer unit, I don’t know if there are any effective aftermarket addons, but it might be worth looking into.
What is your objective? Just to make ice or keep something cold using ice? If it is the latter, just save the middle steps and get a propane cooler. http://www.propanecooler.com
Try using a freezer for a sailboat. Of course then you need a battery and either solar power or wind generator…
http://www.myboatsgear.com/mbg/product.asp?prodID=1565
Thank you all! Looks like a propane refrigerator is the most practical one after all. I am going to stockpile propane cylinders as well.
Worth adding, the proper answer depends upon how serious you are about really getting a capability that is independent of outside energy sources. The OP read as rather flippant, so you got a whole range of hypothetical answers. If you really want a solid long term capability is is likely that an array solar voltaics and a conventional refrigerator will be hard to impossible to beat. You could reasonably expect it to run for tens years, and probably longer. There is zero chance you can lay in enough propane cylinders to match that. A conventional refrigerator is pretty efficient, and if it is well insulated can be very good. If you are freezing a lot of water you are more worried about the energy to do the freezing than the energy needed to keep frozen, and here a conventional refrigerator will be unbeatable. You also get the added flexibility in having a personal source of power for other things. This was explicitly outside the scope of the initial question, but so was a propane refrigerator.
That was a big business in New England through the 1800s.
I also remember reading that, in North Africa during WWII, U.S. Army Air Corps pilots would take a bomber loaded with beer up to 30,000 feet and circle for half an hour or so, then land with the nicely-chilled beer.
How on earth does that make ice?
You could always rig up a bicycle to power a generator. Get Gilligan to pedal, but keep a close eye on him.
Or if you had a lot of hamsters…
The water and the ammonium nitrate react endothermically, in other words the reaction absorbs energy (heat) from the surroundings.
Move to a mountaintop.
There are multiple stages to a post apocalyptic world, a generalization could be 1:start with living off reserves of working items then 2: coming up with improvisations out of non-working or non-desired but possibly still working items to 3: starting a new society no longer dependent on living off the old.
Using a propane freezer would work with #1, using a water wheel to drive a compressor would work with #2, and using the storing natural ice or making a radiant clay pot cooling dish would be #3. So just be prepared to switch methods along the way.
Very interesting. Apparently this is the reaction in cold packs. I wonder if the solution can be dried and the process reused. In a hot environment the drying part should be easy.