Based on my admittedly limited experience, I would think it is near on impossible to keep your feet dry when it is raining.
Overshoes keep water out to a point but it's damage limitation really. For me, and as bonj says, their purpose is really to keep the feet warm. Plus, I have yet to read any review of a winter shoe that states the feet are kept 100% dry after a significant length of time. As for waterproof socks, if they did work I think they'd probably be boil-in-the-bag such is the nature of the fabrics.
Personally, I just accept that my feet will get wet sometimes and so long as they are warm then I don't overly mind.