Frosting does wonders in helping you store your baked goods. When your cake is frosted, it acts as a "plastic wrap", and helps to keep your cake moist. To store your frosted cakes better, you can cover the frosted cake with a larger bowl and place it in the refrigerator. Another tip that can help you keep your frosting in place would be to place it in the refrigerator for 15 - 30 minutes to allow the frosting to set, before wrapping it and placing it back in the fridge. This way, you won’t have to worry about your frosting being messed up. Just remember to allow your cake to thaw when you take it out before serving!
With cut cakes, you should cover the sides that are exposed (i.e. the cut sides), with plastic wrap. This will reduce the moisture lost by the exposure. The rest of the cake can be treated as an uncut cake.