Well, that isn't quite a fair comparison, since the ice-fan only cools the small column of air between the fan and your bed, while an air conditioner cools all the air in a room or building. That said, the ice-fan is probably more efficient than a very small air conditioner than performs the same level of cooling (not that such small air conditioners exist), whereas an air conditioner is surely more efficient than the quantity of fans and ice that would be required to cool an entire room or building.

I have another question, since my basic physics knowledge is a bit lacking. Compressed refrigerant system like air conditioners work by expending (electrical) energy to move heat from one system (the inside air) to another system (generally outdoors). With the ice-fan, where does the heat go? This is probably a fallacious way to explain it, but is the energy being removed from the air and used to transfer the state of the H20 from solid to liquid? And if that's the case, if you wanted to cool an entire room rather than a column of blown air, you'd have to have the liquid water end up outside the room, just like the exhaust from an AC system is outside?

With the ice-fan, the heat from the room is going into melting the ice (and, eventually, warming that water to room temperature).

The freezer, of course, works just like an AC: it moves the heat from inside the freezer to outside the freezer — i.e., to the room its sitting in (some large commercial freezers actually use outdoor parts so then can dump the heat outdoors). Assumably, during the day, the windows are open, so that heat will escape outdoors.

Random note: If you could prevent all heat transfer with the outdoors, the freezer/fan/ice cycle would actually heat the room.