Playhouse to sauna conversion
No, you do not need to remove the drywall to install the sauna. However, you will need a foil barrier (to reflect the heat back into the sauna) installed over the drywall. I'd install insulation on the wall too, to isolate the sauna from the house. 

The reason you use cedar boards is because the room will heat up and expand then contract 
making big cracks in drywall. The cedar boards will resist the rotting associated with the wetting/drying process and "move" with the heating/cooling process. 

I've never used cement board for a floor. 

Make sure you have a "wet location" light and enough venting (outside air intake). Your toughest task will be finding an appropriate sized heater...too small and it'll never heat the space...too big and you won't be able to be in it very long. 

If you google, "how to build your own sauna", they have a zillion sites to help you.