I don’t refrigerate mine. The risk from bacteria is virtually nil due to the very high sugar content. Similarly it inhibits moulds, which will take many weeks to form. Refrigeration will inhibit the moulds too, but if you’re using your icing over one week, it’ll make no difference.
I will also keep icing in its separate colours for months if they’re just for non-edible projects, but the quality does deteriorate. I find it becomes more porous, less smooth and shiny, and softer so difficult to use for painting, or fine piping details which need strength.