I can't comfortably fit thick socks in my cycling shoes either, but here is what works for me in cold weather.
I use a pair of Pearl Izumi shoe covers - mine are old, but they are the equivalent of the AmFib shoe covers. If it's really cold, I add toe warmers (stuck to the bottom of my socks). The toe warmers I use are called Heat Treat Toe Warmers. Here's a link to the product description on the REI web site, just so you can see the details: http://www.rei.com/online/store/Prod...ory_rn=4500521. Maybe you can find these (or something similar) a little closer to home!
--- Denise