I dress in many layers. For my feet I put on a thin pair of cycling socks, followed by one or two pair of very thin wool socks. Wigwam makes excellent wool blend Ski socks that work well, and last forever. Over the socks I always wear Gore-Tex socks. These keep out the wind and help keep your feet dry.
Shoes are next.
You need a pair that are about one size larger than you normally wear. They must fit over all of these socks without cutting off circulation to your toes. The last layer for your feet are booties. You can cut a hole in the sole for clipless pedals. Don't use toe clips and straps.