Interior wood stains are formulated for interior use and do not contain UV absorbers, mold retardants or HALS (Hindered amine light stabilizers used to protect the polymers from the effects of photo-oxidation.) Waterbased interior stains are much more likely to fail.
You could try this look on an exterior door that will not receive a lot of sun, but be prepared for more maintenance than usual. It is not recommended.
Everyone should note that all exterior finishes need to be maintained at some point - MOTHER NATURE wins the longevity war