Water ice is observed to order at the copolymer ferroelectric poly(vinylidene difluoride-trifluoroethylene) surface. The successful growth of crystalline thin films of water on these polymer surfaces implicates water to polymer dipole interactions. These ice thin films are sufficiently ordered for experimental identification of the wave vector dependence in the electronic band structure of hexagonal ice. The significant band dispersion, of about 1 eV, suggests strong overlap of molecular orbitals between adjacent water molecules in the ice film. The presence of dipole interactions with adsorbate water is consistent with the possibility of water acting as a spectator to surface ferroelectric transitions in this system.