A periodic Hartree-Fock nb initio study is presented concerning two proton-ordered structures of ordinary ice : one ferro-electric (C-ice), the other anti-ferro-electric (P-ice). The calculated energies are practically coincident, and in good agrement with the experimental stability of disordered ice Ih. Slabs are cut out from these crystals in order to formulate a model for studying the surface properties of ordinary ice. The stability of these two-dimensional periodic systems is discussed, and the relaxation of the P-ice slab formed by two bilayers parallel to the (001) face is considered. Finally, an embedded cluster method is adopted to calculate geometric and energetic properties of KOH and NaOH dissolved in C- and P-ice at low concentration, This study permits us to discuss the role of KOH in promoting the transition from disordered Ih to ordered C-ice, which has been observed to occur at 72 K [Leadbetter et al., J. Chem. Phys. 82, 424 (1985)].