I ride an hour in the rain somedays to and from work. It is Oregon afterall. I tried plastic shopping bags on my feet and that does work, but there is a wicking effect that happens when your pants get wet and they soak into your socks. The water tends to migrate into your shoes. I got a pair of shoe covers and that helped more, but I still have the wicking effect.
The wicking effect seems not to happen if I wear some kind of gator over my pants and show covers. This would then allow the rain to slide off and not migrate into my shoes.