Our current water heater (gas, tanked) is installed in a little enclosure on our back patio. We want to replace it with a heat pump water heater. We live in Southern CA. It never freezes. Everything I read about them assumes they will be installed indoors. Seems to me that it should be OK if it's outside as long as it is properly vented and protected from the rest of the elements.
A specific example is this Rheem. The installation documents say "Do not install in outdoor, unprotected areas". It also says "It is recommended that the hybrid water heater be installed where ambient temperatures DO NOT exceed 145°F". Which kind of leaves open the option to install outdoors in a protected area (emphasis mine). But nowhere does it explicitly say that outdoors and protected is acceptable.
Our summers are hot but it doesn't get anywhere near 145°F where we would install this. I guess my primary concern is still the temperature (which maybe gets to 110 on a bad day). But going strictly by the documentation it sounds like this would be OK.