What prevents ice from being an electret? My question is apparently simple: if we put water in a electrostatic field and leave it to freeze, while still in the strong electrostatic field, to make ice, why wouldn't this ice exhibit electret capabilities?
 A: In the structure of ordinary hexagonal ice at low pressure, each molecule is held in a sort of tetrahedral cage by its four nearest neighbors.  It acts as donor to two hydrogen bonds, and acceptor to two more.  You might get the wrong idea that it can have any of $\left( _{2}^{4} \right)=6$ possible orientations, but the orientation of each molecule is constrained by the orientations of its neighbors.  (There is some freedom, but flipping one molecule induces a cascade of flips.)  In the absence of an applied electric field, ice has no overall dipole moment.  
An applied field would, of course, induce enough polarization to give ice its impressive dielectric constant, but the polarization is not frozen in.  If the applied field is turned off, the molecular orientations relax in roughly a microsecond, as inferred from the frequency-dependent dielectric constant.  (The relaxation time is roughly $10^4$ times shorter in liquid water.)
It is not unreasonable to suspect that an applied electric field might favor one of the alternative structures observed at extreme pressures, which have less orientational entropy, but don’t forget that the overall dipole moments of electrets get neutralized by surface charges attracted from the environment.
A: If I'm understanding your question correctly, then it seems like you're asking why ice is not a ferroelectric material. In classical physics, dipoles interact in such a way that their dipole moments have less energy when they're aligned in opposite directions. This is true for both electric and magnetic dipoles. Therefore classically we don't expect ferromagnetism or ferroelectricity to exist. They can exist only when the quantum-mechanical properties of the orbitals near the Fermi level are unusual. So if your reasoning is that if water molecules are dipoles, then solid water should be ferroelectric, then that implication just doesn't hold.
A: When water freezes, the water molecules are in a specific arrangement (see hydrogen bond, ice).
While it is true that exerting a strong electric fields can alter the freezing point, when it does freeze in the strong electric fields, the molecules will still in the specific orientation, and hence not demonstrate additional dipole polarisation. 
