In the deepest freeze of winter, I bring the ducks fresh water in their 2 gallon stew pot. The first hour they spend washing up. Then I replace that water, and the rest of the day they drink out of it. This was their idea, I just observed and caught on. Then on unusually mild days I will fill a swim pan for them.
Draining the hose in the late afternoon is key for me. I did it last night, but not properly, so I filled the hose with water this morning and it froze. drat. I will get my winter mojo back.
And eggs can be frozen. I open them and stir them up, mixing yolk and white, and then freeze them. Some folks use ice cube trays, one could use custard cups, cleaned-out small yogurt cups. I like to freeze things in them and then pop them out into a gallon-sized freezer bag.
Some folks write that you can dry the eggs in a dehydrator using the fruit leather tray, then put pieces of that in a blender and make powdered eggs. Extra effort, but you don't lose it when the electricity goes out (which it has hear more and more often).