Ya pretty sure there's no issue using them in the rain. Or they wouldn't sell so well up here in the Pac Northwest!
I use them year 'round on job sites. They are not kept under shelter. Rain or shine. They don't even get maintained, other than adding oil if the low oil sensor shuts em down!
I've found they don't run well under water! But as long as the water level is below the intake they keep running!