First up is my declaration, stay safe above all else! I do not advocate shooting outdoors during thunderstorms. Please heed, Carbon Fiber is a great conductor.
Why would you want to go shoot while it is raining? Color Saturation, very even lighting, and awesome reflections to name the top three reasons.
Things to watch for: Diminishing weather conditions. Don't hesitate to pull out if you see the weather going badly.
Equipment: Keep it simple. Carry just what you really need.