Snow is a great insulator, so she will be fine and if her body temperature stays up those eggs will be tucked in the warmest crevasses of her body. I have never figured out why nature has birds of prey mating and producing young at this time of the year.
I have wondered as well. However, they breed and nest in the winter.
It must have something to do with the time required for the young to be self sufficient by the next winter
I would guess that there is plenty of food to be caught in the spring from all the other births in the animal kingdom.
and surprisingly there are large numbers of bald eagles in Alaska!