No socks with ballet flats, unless you can't see them (nude nylons or "no-show"/liner socks). If your ankles need more warmth, it is time to wear boots or to wear loafers or something with a much higher vamp.
I mostly wear boots in the winter time. I find them really comfy. I also have Merrell's (Encore Ice or Chill?), and old-school Bass loafers for weekends.
Personally, I find it easier to wear boots, as then I don't have to think as much about matching my socks to my pants or shoes. Laziness wins.