Proper winter cycling boots are warmest: Lake MXZ302, Specialized Defroster, Shimano MW81 etc
Neoprene overshoes are reasonable, but you'll have to replace them every year if you use them much.
Just putting warm socks on generally doesn't work. It's not the sock that keeps you warm, but the air trapped in the thickness of the sock. If you put thick socks on and wear your normal summer shoes, the air gets squeezed out, and the extra tightness restricts the circulation in the foot which makes things even worse.
You ought to have specific winter shoes that are a size or two larger than your summer shoes, to leave room for thicker socks without squeezing your feet. It helps if they don't have mesh ventilation panels in them to let all the warmth out and water in.