dumb generator question

If you're concerned, take along a small square of plywood and a couple of 2x4's and make a cheap roof.

My Honda 3000i has a warning label to not operate in the rain or wet conditions. But I've done it many times, without finding a way to electrocute myself.

The engines are fine to run in the rain, I would be more concerned with the actual electricity generating parts. You don't want those getting soaked.

I would avoid running a generator in the rain unless it was an actual emergency and no other alternatives were available.

Depends on the brand of generator you're using. Most Honda generators would operate well in the rain although it is possible with the cheaper brands to have running problems with wet ignition components. Just don't cover them with plastic as this will restrict the air flow for cooling them.