We need a lot more info about what exactly you have to be of much help. That said to cover the basics an oven needs to stay dry, and given that it needs some sort of water proof covering. Anything from a "house" with a traditional roof of some sort to water proof stucco are common. The stack also needs a proper cap on it to keep water out. If the oven itself(the insulation and oven core) is wet you do not need to re-cure, but it will take lots of firing to dry it out. You certainly want to fix the water issue before doing it.