Water fowl are amazingly cold tolerant. I have never had a goose with frost bite. Their circulatory system is adapted to dealing with cold weather. So as long as they have good circulation and a full layer of down they cope very well with winter. The only times my geese seemed the slightest...
When you bring them in at 4:30 you don't really need to keep a light on if they go into the coop willingly, but it would be fine to put a light on a timer if you want as long as you secure the cord.
They definitely need clean water deep enough to dunk their head and drink all the time. It...