When it’s cold, one of the biggest factors is wind chill. Wind can make things miserable for anyone, including geese. Build the shelter to limit wind as much as possible.
Make sure it’s got a roof with proper ventilation. Don’t put the water inside of the shelter because it can spill and make the floor wet and colder for when the geese lay down.
Keep the floor warm with hay or wood shavings.
This will help keep their feet warm and prevent frostbite. They’ll be better able to regulate their temperatures because covering their feet will be easier.