Could I freeze this type of frosting when it has already been spread on the cake?

I'm going to make an ice cream cake that must be finished by Wednesday night and I don't have the daytime to work on it. However I want to use this frosting for it: a href="http://allrecipes.com/Recipe/Sturdy-Whipped-Cream-Frosting/Detail.aspx?prop31=1" rel="nofollow"http://allrecipes.com/Recipe/Sturdy-Whip…/a Could I ice the cake the night before (piped and decorated and all), freeze it, and serve it the next night without worrying? (I'm wary about possibly getting strange textures in the icing from freezing, etc.)