Yes freezing a cake does make the cake more moist and makes the cake more delicious as well.
Professional bakers also recommend freezing a cake after baking the cake to make it more moist and when you do freeze the cake it should not harm the cake.
I have frozen cakes after baking them and they did turn out more moist and much better tasting as well.
Wrap the cake in some plastic wrap and then place the cake in the freezer overnight and then when ready you can frost the cake.
When you pull the cake out of the freezer it should be moist as it thaws out.
I always have and always will now freeze cakes after baking them if I don't plan to eat or serve the cake that day.
If I make the cake that day and need to serve the cake that day I will just allow the cake to cool down and then frost it and then serve it.
But if I can bake a cake a day or two before then I will freeze it with some wrap and then frost the cake the next day or on the day I'm gonna serve it.