I believe such freezing is normally done at eight cells, no bigger. And you can in fact remove one of the eight cells and the child develops (apparently) normally - it's the one sure-fire way to sex-test an embryo (recalling from memory).
What we're talking about here is not making sure you can grow a brain at all (the embryo) nor making sure a filter can filter again (the kidney), but preserving the information that makes you you. It's a different kind of problem from getting a filter to work again. The people who actually work with this stuff day to day and would love to be able to recover state from preserved neurons, even in principle, say it's literally impossible with the present state of the art.
http://www.strike-the-root.com/51/walker/walker12.html
Came across it pretty randomly, I found it quite intriguing. Cryonics is "routine" for human embryos, not far-fetched for humans at all. Makes the whole thing seem potentially very reasonable (and me someone who hasn't signed up and doesn't plan to).