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.
Building an outdoor oven for Aaron, I asked the Mason Heater group ...
What do you who build outdoor ovens think about covering the insulation with plastic or some other waterproof membrane before fitting wire lath and plastering the oven?
Nobody liked the plastic idea. Lars Helbro recommended a "coat" of clay/chamotte. I responded that I would probably just use an Acrylic stucco and make it as watertight as I could which elicited an education on "stucco" from Jason Temple ....
It is my opinion that the "stucco" will give you best performance if its lime based. The drawback is that it would need lots of time to cure prior to applying a modern sealer. Common products or formulations that are called "stucco" but are based on Portland cement will reliably have countless cracks, micro and/or otherwise. Well, maybe epoxy based coatings give the truly most impervious performance, but yuck!
FWIW, I would suggest exterior applications of plaster-like materials be referred to as "renders", interior applications as "plasters", and applications that no one will ever see again as "parges" (except maybe a chimney sweep :-)) Stucco is actually pretty specific in referring to Italian traditions of plastering with lime and fine marble aggregates.