Cob is a natural product made of clay, straw and sand.  As such it can be prone to the elements.     It’s optional whether you protect your Cob Oven from rain, hail, snow etc – but be prepared that if it gets wet – it can rot, break, crumble.    We would highly advise to build some sort of protection over your oven as soon as you can.  We put our roof over half way through the building process.      For our roof it is a simple four hardware posts cemented into the ground and topped with an angled corrugated tin roof – a lip over the front allows you to mildly keep dry if cooking in the rain.  The chimney poke out through it.     (that was a bit tricky as we created a hole – but needed to seal it up to allow no rain to run down it onto the cob.   Google searching on how to install flues in roofs will lead you in the right direction of the materials you need to do that).