Which is why you dress for being warm and wet. I'm commuting by bike every day in London and it's usually been between -2 and 2 deg C in the morning/evening the last few months (with occasional milder spells).
I use arm roubaix backed lycra arm and leg warmers. They're not waterproof and they get wet quickly in rain but you soon warm up the water that gets trapped and then you're fine. It's the same principle as a wetsuit.
Getting the number of layers right is tricky. Too few and you'll be cold. Too many and you'll soon start to overheat. The ideal is starting off feeling cold but warming up within 10 minutes of the ride. Warming up much sooner than that usually means you've got too many layers on.
A waterproof jacket is good but don't expect it to keep everything out, so a tight base layer (e.g. Skins) on the torso can be good.
I've done several 24+ hour rides in constant rain with temperatures below 5 deg C using this strategy with no problems.