Figuring out the way the brain connects to the body and reconnecting all the individual nerve connections makes the challenge much harder.

I study neuroscience. You may know something I don't, but I think body transplants would be a lot easier than resurrecting the dead, as long as you save the first few sections of the spinal chord as well - repairing broken spinal chords, albeit imperfectly, is somewhat in the realm of current technology. If we're talking magic, I don't think spinal chord injuries would even be a big deal.

Edit: never mind everything written below about the freezing

I was quite disappointed when Harry just froze her like that. The rapidly expanding ice will destroy much of her data - in real cryonics you pump 'em full of antifreeze to prevent this. Even if he revives her, she might not quite be the same now. He should have transfigured her head into a small crystalline structure and later found some way to securely maintain the spell (and if no one knows he did it, the pesky authorities won't try to take off the spell).