Your girls will lay eggs at any time of the day, and sometimes a pullet will drop an egg from the perch at night, rather than retaining it until she can put it in a nest box in the morning. (I consider new pullets to be like potty training toddlers. They don't quite have the whole process mastered yet.)
If you put your general location in your profile it will help folks to connect with you in a climate appropriate manner. I'm also in "North Country". Luckily, I am able to go out and collect eggs frequently. I make it a point to be sure to check the nest boxes after all birds have gone to roost at night.
To help avoid frozen eggs: Lots of bedding in the coop. Lots of natural lighting. I have 2 thermopane windows on South side, and a full length glass thermopane insulated door, and a thermopane window on the East side of my coop, so it warms up quickly in those cold sunny mornings. Finally, LOTS of hay or straw in the nest boxes, and decrease the number of available boxes in the winter so the eggs are more apt to be warmed by the next hen instead of sitting alone in a nest while the hens use other nest boxes.
As for using frozen eggs: If an egg is clean, and the membrane is not broken, I will use it for baking or any other "completely cooked" purpose. But, the texture is altered. If the membrane is broken, or the egg is not super clean, my dog or the chickens get a cooked egg.
