[calambrac]

No doubt there's still an additional cost, I just don't think it would be high enough to make it more expensive than running an air conditioner, given that you're going to be running the freezer regardless (depending, of course, on how much we're talking about. I'm picturing a window unit vs. a window fan with a baking pan's worth of ice).

Any ideas on how to be more rigorous about thinking this through or running an experiment?

[swombat]

You could take a certain quantity of ice, figure out how long it takes to melt under a fan in hot weather, then calculate the energy required to get that quantity of water into ice (heat capacity equations), and you'd have a rough figure for energy spent per unit time.

Then compare that with the energy consumption of an air-con unit.

[derobert]

An experiment is easy to run. Obtain a Kill-a-Watt or other power meter, then measure (a) how much power the freezer uses over a day w/o freezing extra ice for fan-ice cooling, repeating several times; (b) how much power the freezer uses over a day with freezing extra ice for fan-ice cooling, repeating several times; (c) how much power the fan uses blowing over the ice; (d) how much power an AC uses to keep the room comfortable, repeated several times; (e) [bonus] how much power an AC set to a higher temp. + a fan blowing on you uses to keep the room comfortable, repeated several times.

You can then compare (b)-(a)+(c) vs. (d) or (e).

Ideally, you'd do these experiments in identical conditions (temp., sunlight, wind, humidity, etc.), of course.