The secret to remaining dry has little to do with fabrics.... it is about ventilation. Exercise/cycling will cause you to sweat. To stay dry... you need to evaporate the sweat as quickly as you produce it.

Wool naturally stagnates air movement.... by locking air in the tight little coils of wool fibers. The stagnation is complete enough it will even hold water/sweat against your body keeping you warm.

I'd use layers of moisture dispersing technical fabrics. At lease two layers... three might be better.

Then carefully select an additional outer layer. I normally use a rain and windproof (non-insulated) outer layer with multiple zippered vents. Allowing for LOTS of air-flow that will evaporate any moisture that the tech fabric moved to the outer most layers. You won't get wet.... or even warm. You'll feel cool or close to cold. Regulate the zippered air flow and your activity to control your warmth.

NOTICE: The clothing described in no way will provide you with the warmth needed in freezing temperatures to stay warm if you for any reason... you stop moving/cycling. Having a trunk bag or rack of some sort is essential for foul weather cycling. You'll need to have a coat along if for any reason you break-down or are injured.