I park my bike exposed on the street, and have ridden extensively in the rain. I have had some water in the area of the battery terminals (so protect those) but it hasn't caused a short to the best of my knowledge. I did have a short concurrent with a rainy period, but I cured it by better insulating a few dodgy stretches of wire that appeared to be rubbing, so I think rain was unrelated.
I do have a bit of corrosion on some of the hardware (mirror bolts, screws that hold in the pillion seat, etc), but the bike itself seems to be fine.