I wear the same gear, wet or dry. I will get wet with sweat or rain, doesn't matter, but I don't want to overheat. If it's super cold and dry, I will wear a pressure suit under a vented jersey, otherwise it's a vented jersey, waterproof pants for cold rainy/mud race, vented pants for warm rain race, and outer protection (elbow guards and chest protector).
I wore a rain proof jacket ONCE during a race, got too hot in spite of the 30*(F) weather. Now it's vented gear every race, I adjust pants for temperature. If it's super cold I wear an undershirt, but that's not typical.