The only way a cake can become frosted is if air gets at it, and it gets freezer burn. You couldn't have wrapped your cake securely enough. You have wrap your cooled cake with plastic wrap tightly, then tin foil. I have done it hundreds of times. Perfect results everytime. Of course, I am asuming I am much older than you, so have the benefit of years of experience.
Freezing cakes is a must sometimes because of busy schedules & time constraints. Your schedule makes sense, and when I have the time, this is what I do. But like I said, our schedules don't always make it possible.