What’s your general location? What is a “cold winter” there?
do you have anyway to have electric in the coop or run?
is the run covered at all? How much snow in the winter?
what is coop like? Size, height?
these answers will help give you a variety of suggestions from people in your same or similar climate/winter conditions.
we have electric in our coop. We use a heater base that is made for the double wall galvanized waterer we have. The water stays in the coop in winter. In warm non-freezing temps, water is in the run in the shade. We normally only provide feed in the run, however in especially cold weather (below zero), we do provide feed in the coop bc they generate heat through eating and they only eat with light, so we try to maximize their ability to eat for warmth During the coldest days.