Yes a water heater can be installed outdoors but with a several caveats. First, indoor water heaters are designed to be indoors and exterior water heaters are designed to be outdoors. I wouldn't just stick my indoor water heater outside and expect it to last the designed lifetime. Outdoor water heaters have better paint and seals to protect it against humidity in an outbuilding and rain, sun, etc. if truly exposed. Second, you live in Oregon which I am unfamiliar with winter temperatures but if it gets below freezing, you would also need to heat the enclosure to prevent pipes, condensate lines, etc. from freezing. Finally, when anything with wires and sensitive electronics is outdoors, one must contend with insects and rodents which can play havoc on things.
I have only seen such setups down south where it is quite common to see utility equipment outside the house, usually in enclosures under car ports so they are only exposed to humidity.