I have a pair of PI toe covers that fit fine over my Look cleats, but they make my feet even colder because they cut the circulation to my toes. For me it's full shoe covers or nothing. (Sugoi, and they fit fine over my cleats too. But you should be able to enlarge the cleat hole if you need to.)

#1 rule of warm feet is nothing can be even the slightest bit tight. You may find that your feet are warmer in thin summer socks, if thick socks take up too much room in your shoes.

In a pinch you can put plastic bags over your socks, inside your shoes. It's amazing how much warmer your feet stay just from blocking the wind.