[derobert]

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.