Hey Kinderchicklets,
Its very good of you to be concerned about Princess and Ivy and the eggs. It was alot of snow wasn't it? But even though there was alot of snow, there wasn't alot in the nestbox, just enough to get Princess all snowy while she was incubating.
As for the eggs, they will be fine. Princess is a very experienced mother and she knows how to keep her eggs warm underneath her and she has taught Ivy how to do it as well. (Remember, this is only the second time Ivy has had eggs to take care of - Princess has had eight years to practice!).
If you want to try an experiment, try this. Tomorrow morning when you wake up and you are all warm under your bed covers or duvets that is what it is like for the eggs under Princess. When you get out of your bed, slip out from under your covers/duvet and make your bed but be very careful not to let the warmth escape. Then go off and have your breakfast or get dressed or whatever you do first thing. Then come back and carefully put your hand under your covers again - it should still be warm under there - the covers/duvet will have trapped the warmth from your body. That's what happened with the eggs when it was snowing on Sunday. Princess was using her body and her feathers to keep her eggs warm. When she had to leave to get some food, Ivy would come quickly into the box so that he could use his body and feathers to keep the eggs warm like your covers/duvet did when you made your bed. When the weather is cold, Princess and Ivy don't leave the eggs uncovered for long so that they can trap the heat and then the eggs don't get cold. When its warmer, like today, they might leave the eggs uncovered for a few minutes because they sun will help to keep the eggs warm. If it gets very hot, Princess and Ivy will have to use their bodies and wings to keep the eggs shaded so they don't get too hot! That would be like taking a nap in your snowsuit on the beach in the middle of the summer!