OP
SpitfireW'sale
As long as the inverter (and everything else) is IP rated it's fine. theft is the only possible issue but even that can be mitigated. No need to put the inverter in a box, and it would need to be a very big box to maintain airflow.
We looked at supply of just such a box for security on external mounted inverters, but it brings warranty issues to the fore. The concept works with a well vented box to allow for airflow, but depending on the inverter, the manufacturers recommend approx 50cm radius with no obstructions. Even if your box is well vented, if it does not comply with their recommendations, they are unlikely to pay out if the inverter does fail inside of warranty limits.