I live by freezing. You can definately freeze a cake—and I freeze them frosted. I think it protects the cake, even.
What I do is this:
FREEZING A WHOLE FROSTED CAKE:
1. Frost, etc., the cake. I usually frost it right on the surface of my cake carrier. If you are going to put it on a platter you can’t put in the freezer, put a layer of parchment under it when you frost it so you can peel it off later.
2. Put it in your freezer (uncovered). You can also refrigerate it as a middle stage, if you want, but I usually don’t. I put the whole base of my cake carrier right in the freezer. If yours is on parchment, then put the parchment on a stable surface (like the cardboard round from a frozen pizza) so it supports the cake.
3. When it’s nice and firm—a few hours—take it out and wrap it nicely with plastic wrap. A frozen cake can stand a lot of wrapping and mild handling, so it’s fairly easy to wrap. I just wrap it around several times and then make sure some the plastc wrap will be “sealed” when I put the lid on the cake carrier (squashed between the lid and the base). If you’re using the “parchment method”, you can wrap the whole cake.
4. Put the lid on your carrier and put your cake carrier in the freezer. Or if using the parchment method, wrap it in foil.
5. Two days before you want to eat it, put the cake carrier in the fridge. I’ve frozen up to a week this way no problem. Can easily go longer. If you used the parchment method, and have to handle the cake a lot to unwrap it, you might want to do that when it’s frozen before you put it in the fridge and just gently drape it with wrap in the fridge.
6. Take off the plastic wrap and put it on the counter to thaw abouy 6 hours before you want to eat it if you want it at room temp.
Put it in approx. 2c plastic containers—leave as little headroom as possible—and freeze them
Put them in the fridge 2 days before you want to use it.
The night before you want to use it, take it out and put it on the counter to come to room temp.
The main thing for both is to give about 16 hours from freezer to fridge, and then about 6 hours on the counter to come to room temp.
Beware of using frozen buttercream that is not totally at room temperature. Leave your house if you must, but don’t touch it until it’s room temp. Feel free to go 8 hours or even 10 rather than less.
Cream cheese frosting is considerably safer, so you don’t have to worry quite so much. As long as it’s spreadable, you’re good!