The rain would only effect you if you were shooting feathers instead of plastic vanes. Now Tempature can cause problems if the bow gets wet and then freezes. cables can stick to the cam, arrow rests/cushion plungers won't operate, and ice on the arrow can all effect your shot.
Thats why the late Wasatch frount extended season is so much fun.. if it is not raining it is snowing, freezing temps stiffen bow limbs..
I lubricate all moving parts with graphite instead of oils so nothing ever freezes on me.