I thought I'd give it a try. I was convinced that the eggs would crack in the freezer, but I could spare a couple as an experiment. So I washed half a dozen eggs and put them in the freezer in a zip-top bag, labeled with the date.
The next day I checked them out. Yes, they had cracked, but evidently the egg inside was already frozen when that happened so there was no mess.
It was easy to peel one of the eggs after letting hot tap water run over it for a few minutes. It's a strange feeling to hold a shell-less, raw egg. I put the egg in a bowl and stuck it in the refrigerator to thaw.
By the next morning it was thawed and ready to use. The yolk stood tall just like a fresh egg should. I used it in a batch of cookies.
If you have room in your freezer, this is a viable method of preserving eggs. It's less time-consuming than freezing them in ice cube trays, and you are not limited by the number of ice cube trays you might have - I have four but it's never enough for whatever I'm freezing. The main downside to using ice cube trays is that one egg equals more than one cube, so figuring out how many you need for a recipe is a guess.
They should be used within a few months, so it's not a long-term solution. Hopefully the hens would be laying again within a few months, if the "slowdown" was caused by winter's cold, summer's heat, or molting.
Putting Eggs By, Part One
Putting Eggs By, Part Two
Putting Eggs By, Part Three