Of course you can always cover your outdoor oven or keep fixing the inevitable cracks but here's an idea about how to keep the outer shell of your oven weather-proof and crack-proof - from a master oven builder, Norbert Senf, in a Masonry Heater Association chat ...
What I like about silicone is that it remains permanently flexible, even after 20 years of heating cycles. It was used to put the refractory insulating tiles on the Space Shuttle skin, which was titanium. It transfers heat well, and silicone grease is used as heat transfer compound for mounting heat sinks to computer cpu's.
The caulking was siliconized white, which came in a can premixed. Don't know if it is still made. I'd probably use latex from a caulking gun these days.