Q. Can confectioner's sugar be frozen?
Sure. Why? An unopened bag is going to last as long on the
cupboard shelf as in a freezer (which is to say a very long time). We suppose a freezer could provide a drier environment for an opened bag of confectioner's sugar. Perhaps it also provides a refuge from critters, if that is an issue in your part of the world.
Otherwise, we can think of many more important foods that deserve the sanctity of freezer storage, and in our view, there is never enough room in the freezer for some of those items. Confectioner's sugar is cheap and always available you can probably afford to take the gamble and store it on a cupboard shelf.