For me it's the wind chill (and plain chill effect) from cold rain/snow/sleet/etc that affects me.
I ride with a "plastic shell" rain jacket. Sure I get damp inside but for me the key is keeping the wind off of me. It's like the "plastic bags over your shoes under your booties" deal - your feet get damp but much drier than if they got dumped on by water.
For racing in the rain I duct tape the number to the outside of the rain jacket.
If you can find it Fox Racing sold a clear jacket with a full coarse zipper (i.e. easy to use when muddy). I have a Louis Garneau clear shell, that's velcro, and also a Descente clear shell (zipper? velcro? I forget). I've since given away my Fox jacket so I use either the LG or the Descente.
I'd MUCH rather get damp due to sweat than soaked due to freezing cold rain. I'll race with a clear rain jacket even in 50deg rainy weather. I've finished races pretty well (like winning the field sprint) and then watched as other "sleeker dressed" riders shake and shiver their way to their cars.
For me Warm > Dry.
When it's warm and raining I may use a wind vest to keep my torso from getting chilled but if it's really warm (80+ deg) then getting wet isn't a problem.