It is generally accepted that nuclear quantum effects (NQEs) trigger the transition to the nonmolecular form of ice under increasing pressure. This picture is challenged in salty ice, where Raman scattering measurements up to 130 GPa of molecular ice VII containing NaCl or LiCl impurities show that the transition pressure to the symmetric phase ice X is shifted up by about 30 GPa, even at small salt concentrations. We address the question of how the inclusion of salt induces the drastic reduction of NQEs by selectively including NQEs in ab initio calculations of ice in the presence of distinct ionic impurities. We quantitatively show that this is mainly a consequence of the electric field generated by the ions. We propose a simple model that is able to capture the essence of this phenomenon, generalizing this picture to other charged defects and for any concentration. This result is potentially generalizable to most "dirty" ices in which the electric field due to the doping is much more significant than local lattice distortions.