The nucleation and adhesion of ice to solid surfaces plays an important role in a wide range of contexts, from serving as nuclei for clouds in the upper atmosphere to forming on the surfaces of aircraft and ships, reducing their performance. Controlling the formation of ice using additives or novel coatings has, consequently, been a long-standing pursuit in materials science. Here, we employ molecular simulations to explore the nano-scale detail of ice formation on a variety of surfaces and determine what molecular features are necessary to create surfaces that display extreme ice-phobicity and ice-philicity by modulating lattice match, surface polarity, and surface attractions. We further extend these results to quantify surface ice-philicity on chemically and topographically complex surfaces by focusing on the thermodynamics of interfacial water molecules. These results serve as a foundation for future molecular studies of ice formation in all sorts of environments, with the goal of designing materials that can reliably control the formation of ice.