A fun thing my mother did with leftover frosting was to spread it between two graham crackers. Boy were those great eatin'! She would keep them in her cookie jar but they usually didn't last long! Since your frosting needs refrigerated you could keep them in the frige for a snack.
I used to do that with my kids too but they are all grown up now and we don't have cake that often anymore. I may have to get one of those jars of frosting and a box of graham crackers soon just to make these things!