In a word - No. Non food items should not be placed in a food keeping appliance such as a food refrigerator or freezer. One good reason is that someone else may think this is frosting, or other food and try to eat it. Also fumes may permeate the freezer and contaminate your food stuffs.

There have been debates on whether it is best to freeze paste art paints to keep them pliable. If you feel you need to do this, buy a small dormitory freezer and label it "for artwork only".   Keeping air out of your paints may be the best way to keep them workable.  Keep the caps on your paint tubes, only mix what you are going to use, and cover your palate with clingy stretch wrap to keep it from drying while on break.

BTW, My laboratory has two refrigerators - one for human food, the other for lab samples.  It is a lab rule to only eat in the designated areas.  Thanks for your question.