Refrigerators have evaporators to remove condensation, so they will dry out cake.
It's important to start with a moist cake formula. If you have to refrigerate the cake for an extended period of time store it in a airtight container.
If the cake is too tall for a cake carrier, use a brand new clean corrugated cardboard box. Tape the seams to prevent moist air from entering the box. The box must be corrugated as it provides insulation. It will also absorb any moisture.
If the cake is going to be covered in fondant, it's important that the crumb coated cake is de-gased overnight. if you do not degas the cake air bubbles will form under the fondant.
How to de-gas a cake. if you are going to refrigerate a fondant cake, it should be in a corrugated cardboard box for the reasons I mentioned above.