I don't get out running as much as I'd like with DD, but when I do get out, if it is even a little cold, I always use the rain cover. Plus, I have a Kiddopotamus Go Cozy that works really well. http://www.kiddopotamus.com/p_go.php
I dress her in layers and she always seems to do fine. However, I live north of Seattle in Vancouver BC, so we definitely don't get cold winters.
FWIW, DD seems to quite like our Chariot Cavalier and always seems to fall asleep on runs, especially when I use the rain cover.