question: Heterogeneous nucleation of ice from supercooled water is the process responsible for triggering nearly all ice formation in the natural environment. Understanding of heterogeneous ice nucleation is particularly key for understanding the formation of ice in clouds, which impacts weather and climate. While many effective ice nucleators are known, the mechanisms of their actions remain poorly understood. Some inorganic nucleators have been found to nucleate ice at warmer temperatures in dilute ammonium solution than in pure water. This is surprising, analogous to salty water melting at a warmer temperature than pure water. Here, the magnitude of this effect is rationalized as being due to thermodynamically favorable ammonium-induced disordering of the hydrogen bond network of ice critical clusters formed on inorganic ice nucleators. Theoretical calculations are shown to be consistent with new experimental measurements aimed at finding the maximum magnitude of the effect. The implication of this study is that the ice-nucleating sites and surfaces of many inorganic ice nucleators are either polar or charged and, therefore, tend to induce formation of hydrogen-ordered ice clusters. This work corroborates various literature reports, indicating that some inorganic ice nucleators are most effective when nominally neutral, and implies a commonality in mechanism between a wide range of inorganic ice nucleators.