I refrigerate if the icing is going to be held overnight primarily because I often work with raw egg whites rather than with a meringue-powder base. I always cover the icing surface flush with plastic to prevent a crust and then cover the bowl with foil for day-long or overnight storage. If I make the icing with meringue powder, then I don't need to refrigerate it.
I try to use all of my icing the day I color it, however. I find that if I sit the icing in the fridge overnight, the colors don't set as solidly the next day (more speckled and mottled, sometimes). Perhaps this is because the icing picks up some moisture from the fridge? Not sure.