If you come into my kitchen on any given day, you will find a bunch of snap top bowls containing bits of colored frosting.
If you know me, you know I hate waste (the one characteristic that would make my mama most proud). Many bakers toss leftover frosting once they have made their cookies but I don't. That has my buttervan and sugar in there. So, whenever I have enough of one color, I will save it in a bowl by itself because chances are, I will need more of that color tomorrow. Now, if I have just a smidgen of a color left, I squeeze it all into one bowl. It looks like a mess but I have plans for that multi-colored concoction. No matter what colors I am combining, if I stir it all up, it will become some shade of brown. For the longest, I never even bought actual brown coloring because it is so easy to make. However, you will be happy to know that one day I decided that I DESERVE brown so I don't have to worry that this is a little too green or orange or some such. I make black almost every single day. Any leftover colors in the rainbow can be easily turned to black (if not brown). It takes far less Americolor to turn some awful shade of frosting to black than it does to make black starting with white.
One of the things I love so much about flood frosting (other than its taste) is that it only dries when it is exposed to the air. The less air in the top of the bowl, the longer it will keep. Depending on what colors I need the next day, I can turn yellow to orange, or orange or pink to red or lime green to leaf green. Colors are not difficult to mix if you only have a few basics but you typically get better results by purchasing the color you need. You might have a whole gallon of frosting before you get the right shade of red you need for your favorite team. I can easily keep a bowl of leftover frosting for a week, but I have had others tell me they have kept it for a month. Depending on how much air is in the bowl and how long it sits, you might notice a little separation of the syrup or food color. That is resolved with a spoon. If it has gotten stiff while it waited for you to be inspired, add a spoonful of salt water. After stirring, taste it. If it tastes a bit weak, kick it up with a splash of buttervan. There are really no ingredients that will spoil so there is no need to refrigerate. If I haven't used it in a week or so, I usually go ahead and wash the bowl out. Just know that you can keep your frosting because it can always become black and be used on the next cookies you are frosting.
As always, they are your cookies. Do what you want with your frosting. But as for me and my house, we save leftover frosting.