The car plug itself is IP44 rated (says so in small raised letters on the black plastic). This says what its designed for.
https://en.wikipedia.org/wiki/IP_Code
first "4" means:
physical particles larger than 1mm - Most wires, slender screws, large ants etc.
second "4" means:
Water splashing against the enclosure from any direction shall have no harmful effect, utilizing either: a) an oscillating fixture, or b) A spray nozzle with no shield.
Test a) is conducted for 10 minutes. Test b) is conducted (without shield) for 5 minutes minimum.
So I would conclude "no", don't leave anything less than IPx5 out in the rain.... (But I have to admit I have left the plug on in the rain when I didn't notice it raining, so far I've been lucky - careful disconnecting it).
This is for the car plug itself, the box I have not checked.