What do you do with domestic geese in the winter?

Geese will be fine outdoors all year long eating grasses and leftover seeds and grains in farm fields. If you give them chicken scratch feed and wild bird seed mix they will have a good food. You could also remove some snow so they can get to the grass. As you found out they do not care for a shelter and will get moisture from grass and snow if not from the pond. I found that most birds feet are actually very warm perhaps from increased blood flow to keep them from freezing. They do not seem to feel the cold and more than once I have seen their feet frozen to the pond ice.

I grew up around geese and ducks. No matter how cold it got outside, we would see our geese swimming around in the pond. We did provide shelters for our geese, but I think they only really used them when they were sitting on eggs.

You have done all you can do for your geese. If they get cold enough, they will seek shelter. Besides, their feathers and down are natural defenses against the cold. They will be fine.

They will go to sleep in snow and ice , their feet have a system built in which enables them to shut off the blood supply to them(simplest way to explain)so they do not feel the cold in their little feet.