Recently, the premelting and formation of ice due to the Casimir-Lifshitz interaction, proposed in early 1990s by Elbaum and Schick [Phys. Rev. Lett. 66, 1713 (1991)], have been generalized to diverse practical scenarios, yielding novel physical intuitions and possibilities of application for those phenomena. The properties of materials, in particular, the electrical permittivity and permeability, exert significant influence on the Casimir-Lifshitz energies and forces and hence on the corresponding premelting and formation of ice. To address these influences in detail and explore the resulting physics, here we revisit and extend the analyses of previous work with both the dielectric data utilized there and the latest dielectric functions for ice and cold water. For the four-layer cases considered by some of us, the existence of stable configurations depending on the initial conditions has been confirmed, and different types of stability corresponding to minima of the Casimir-Lifshitz free energy are demonstrated. As the new dielectric functions for ice and cold water deviate considerably from those used by Elbaum and Schick, their vital impact on three- and four-layer configurations is therefore being reconsidered.