wool socks with cotton over them

That's the wrong order. The cotton is for wicking any moisture and for keeping the wool socks from itching. Cotton by itself when it is wet won't keep you warm, but the wool remedies that (this applies in mountain climbing and hiking, etc. In the house you might deal with a little persperation). And like I said, the comfort of cotton versus wool against your skin is the reason for wearing layered socks.

SRS