Grout is not waterproof no matter how well you seal it. So you cannot use any kind of wood, it will eventually swell up and crack your grout and tiles will pop off. I think cement backerboard would work fine, and then the appropriate thinset or maybe silicone. I have not personally done a project such as this so I can't advise much more than that. Oh, you might need to still bring it inside during the winter if you live somewhere with hard freezes.