You can, for a little while. A few hours at most. After that, it needs to be refridgerated. The frosting especially will go bad if left out for too long.
If you want my personal thought, which may not be correct, I think maybe in the next day it will ROT and stink. If it's a type of cheese, yeah, it will stink and rot.
Another answer.
Cream cheese...
Well, no, since cream cheese frosting has a lot of cream cheese in it.Could you simulate it? Hmm. you'd need something to give it the cheesy tang. Some sour cream might do it, but too much and it...