I was researching making the same type of concrete for a similar project- an outside stove for cooking BBQs etc- and found examples of people using it for all kinds of things where it would certainly get wet outside and, presumably, freeze. Some were in places with more extreme winters than we normally see.
None mentioned problems/concerns over frost type damage.
The inside of pizza ovens are generally coated with fire clay after being formed- typically using a beach ball as a former.
You could always paint the outside render with one of the smooth sealing paint type finishes.
As for tile adhesive, I think it is resistant rather than water proof. If you really soak it for a long time it will soften. In showers etc, the tiles protect the adhesive add the exposed grout has a limited area.
The stuff used in swimming pools is another matter. There the grout / adhesive is always exposed and is specifically water proof.