Yes sugar is indeed a preservative as is the salt in salted butter which increased the preservative quality.
Well, you are these days supposed to refrigerate cream cheese frosting. However for home use, I don't refrigerate a cake iced with it, never have and never had a problem, been doing this for many years. For a wedding, it will be the last cake I ice or fill. They are just fine to sit in the hall at room temperature though for several hours. I just won't take a chance on someone outside the home. But quite honestly, I think they are fine.
Hugs Squirrelly