Eurasian colored doves are doing just great around here, all winter long. They've already started some courting/nesting behavior this spring, and we're still below zero nights right now.
We regularly get to 20 below for a few days here and there, and occasionally colder. So they seem to handle the cold weather just fine.
Birds obviously don't need open water to survive (pheasants for example). I always assumed they nibbled on snow, but I don't really know.
