It's low teens here most nights and down to 50 below on rare occasions. I've still never had any problems with ducks or geese. Except getting them drinking water when it gets really cold.
Give them a thick bed of straw in their shelter, so they can have some insulations from the cold ground, if...
I'd sure be surprised if you get frostbite on geese. You can't be too much colder than I am here and I never have any problems with the geese or ducks.
Make sure they have a place to get out of the wind and wet.
Pointing out the obvious: geese don't have combs and wattles and they are wearing...