Shortly after buying my second Yamaha ef2000is, we had a heavy duty thunderstorm and massive downpour that just kept going and going. The Yamaha ran for almost 24 hours under an outdoor table that did little to stop the rain (table top was not one solid surface but a series of parallel boards).
Eventually I had to get a cinder block for the little guy to sit on, as my back yard started to flood.
long story short: don't worry about a little rain, it's an outdoor generator, and although they'll never admit it due to liability, it's designed to run in adverse conditions.