If you put your cakes in the fridge it should only be for about 20 minutes, just to firm up the buttercream, but not totally chill the cake all the way through. The cake itself should still be room temperature.
The fact that the cake is chilled all the way through is what is causing the condensation and stickiness to happen. You should cover the cake with fondant either at room temperature or just chill the icing until it firms up a bit.
Leaving the cake in the fridge over night is too long. You should use spreadable ganache under your fondant, it is stable at room temperature, and firm enough to hold up to covering it with fondant without losing its shape.
But if you are set on buttercream don’t let the cake get cold, just the icing.
Good luck.
Teri, Ontario, Canada http://www.TeriLovesCake.ca
