Both the cookies and the frosting freeze well. I sometimes make a double batch of the dough and freeze half for later. Saves a lot of time the next time I want to make these. You can also freeze the baked cookies for frosting later.
Since I typically make a half batch at a time, but make a full batch of frosting, it's not unusual for me to have some frosting left over. When I need it, I take it out of the freezer, let it thaw a little bit, and then stir it well. Use as it is or add color to it. Spreads and tastes just like fresh!!