Well, it is good to get some warm of socks. Either real or synthetic wool socks are a prime choice. They will help withstand some of the wind for being thick and wool is know for staying a good insulator when wet. Both of these characteristics are important since running shoes are made to allow air to flow freely for running in hot weather. I prefer the summer/hiking variety of socks because my feet stay warm, not hot.
Come early spring, these are also useful as icy puddles may have formed from early melting, but still try to avoid it. Not fun.