You can build any style
rocket stove outside but if it gets wet it wont work very well.
So the design must include some way of keeping it dry.
All refractory materials are porous so they will even absorb
water from the atmosphere, if that happens then the stove can easily be damaged if it get hot to quickly!
So yes you can have an outside rocket stove just make sure it has a cover when not in use and be very wary starting up a damp stove.