The successful use of ice-binding proteins (IBPs) to develop anti-icing surfaces requires a comprehensive understanding of their working mechanism when introduced in environments distinct from the protein's natural setting. This study systematically addresses this aspect by investigating how IBPs control ice accretion when grafted onto an aluminum alloy using polyethylene glycol (PEG) linkers of various lengths and on the polymer backbone of a PEG hydrogel matrix. Freezing experiments monitored through thermal imaging reveal that the degrees of freedom of the proteins significantly influence their functionality. Specifically, we demonstrate that when the degrees of freedom of anti-freeze proteins (AFPs) are restricted by their functionalization on surfaces using short linkers or when they are present in restricted volumes in polymers, they behave as ice-nucleating proteins (INPs) promoting ice accretion. In conditions where their degrees of freedom are enhanced (long linkers, water-rich environment), AFPs effectively inhibit ice nucleation and propagation. The work underlines the relevance of protein mobility as a so far unforeseen key design factor needed to fully benefit from the potential use of natural or synthetic AFPs grafted on surfaces for cryopreservation of biological samples and the design of next-generation low-icing surfaces and coatings.