I wear trail runners in winter as well. If I'm going to be hiking in snow/wet, I wear Rocky gore-tex socks while hiking, with a warm sock underneath. I also size up half a size and get extra wide trail runners to accommodate the socks. If it's a dry hike, just cold, I won't wear the Rocky's, just thick socks.
Like Ken, my feet stay warm as long as I'm moving. If I stop my feet get cold, so I don't take long breaks. I also bring WM booties and a dry pair of sleeping socks for camp.