Li-Ion battery questions
I think you might be worried about structural effects of expansion and contraction of the crystal structure of the electrolyte. If that's your concern, you really shouldn't be, especially while the device is off. It is true that intensely low temps could mess things up, and so could intensely high ones. But the temperatures involved in the transition from a typical freezer to high in the operating range of the common lithium battery pack aren't sufficient to cause loss of capacity or structural damage by themselves. Big bloated battery packs happen because of outgassing and extreme internal temperatures near end of life or with abnormal use.

It is true that lithium ion capacity suffers if maintained at full charge or no charge for a long period of time. It seems to do bad things to the crystal structure, and that is still getting researched. I know for fact the newer iPads have oversized battery packs crammed into them, but I don't know how much. I suspect they say 99% on their battery readout when they are at about 90 or 95% of the equilibrium point for the given voltage; that is, they just aren't actually full, so they won't suffer the full charge degradation.