I have to disagree with much of this post. First off, ALL freezing causes moisture to crystallize and damage tissue. The FASTER something is frozen, the smaller those crystals will be and the less damage they will cause. Flash freezing causes almost no damage at all. Also, when frozen properly (as quickly as possible) food often retains MORE of its nutrients than if left alone. Many fresh vegetables, for instance...begin to lose their nutrients the moment they are picked. In the days it takes them to travel from the farm to the store to your own table, they can lose much of their nutrients. If they are flash frozen immediately after being picked (as is the case with most frozen veggies) they retain far more of their original nutrients.
Rodents aren't veggies, obviously, but based on millions of animals being fed frozen prey items over decades and decades of life with no ill effects, I'd say that the tiny bit of nutrients lost in the freezing process is not the least bit detrimental to the predator.
And I'd also be willing to bet that if I fed my child only frozen foods that are whole foods, veggies, fruits, whole grains and organic meats and poultry....they'd be FAR more healthy than any child fed a typical American diet of processed junk food, no matter how "fresh" that junk food may be. Just sayin'....
EDIT: Forgot to add my thoughts on the original topic: Freezer burn is not harmful in any way. It's just distasteful to human sensibilities. It may, however, cause the animal to smell different and increase the chances of refusal for some finicky eaters.