Electronic and vibrational contributions to the static and dynamic (hyper)polarizability tensors of ice XI and model structures of ordinary hexagonal ice have been theoretically investigated. Calculations were carried out by the finite field nuclear relaxation method for periodic systems (FF-NR) recently implemented in the CRYSTAL code, using the coupled-perturbed Kohn-Sham approach (CPKS) for evaluating the required electronic properties. The effect of structure on the static electronic polarizabilities (dielectric constants) and second-hyperpolarizabilities is minimal. On the other hand, the vibrational contributions to the polarizabilities were found to be significant. A reliable evaluation of these (ionic) contributions allows one to discriminate amongst ice phases characterized by different degrees of proton-order, primarily through differences caused by librational motions. Transverse static and dynamic vibrational (hyper)polarizabilities were found by extrapolating calculations for slabs of increasing size, in order to eliminate substantial surface contributions.