Do we have to bake another cake?

My brother's birthday is tomorrow, and my present to him is a home-made ice cream cake. We froze the cake part when it was finished (not the ice cream), after it cooled off a bit, this morning. When we went to take it out to put it together with the ice cream and frosting, ice had formed on the cake. It has since thawed, it is currently in the fridge. We made the cake in two 9 inch circular pans. My question is, will we need to bake a new cake?