Does Buttercream Frosting Need To Be Refrigerated?

If it is made with milk and butter does it need to be refrigerated?? I usually use the Wilton recipe (with just crisco and no milk) but I have discovered that when I use butter and milk it tastes sooo much better! BUT its going to be used under my fondant and I can't put the fondant covered cake in the refrigerator so is it ok to use the buttercream w/ milk under the fondant???

Sometimes the fondant sweats a bit when you first take it out, but it drys up. The only fondant I don't like to refrigerate is fondant that is painted on with food coloring (Ex: a fondant figure with the eyes painted on) because if it sweats it will make the paint bleed.