Hyperactive insect antifreeze proteins and bacterial ice-nucleating proteins are arguably the most potent ice-binding molecules in nature. These highly effective proteins bind ice through amphiphilic ice-binding sites based on arrays of threonine residues. It remains poorly understood how hydrophilic and hydrophobic groups of the binding site contribute to the ice affinity of proteins. Here, we use molecular simulations to demonstrate that the hydrogen-bonding and hydrophobic groups at the ice-binding site of the antifreeze protein TmAFP of Tenebrio molitor and extended ice-nucleating protein surfaces contribute distinctively yet almost equally in magnitude to their binding free energy to ice. The methyl groups rigidize the ice-binding site, slow the water dynamics at the ice-binding surface, and stabilize the clathrate-like water in the anchored clathrate motif that binds these proteins to ice. We find that hydrophobic dehydration of the methyl group does not contribute to the binding free energy of the protein to ice. The role of the hydroxyl groups is to anchor the clathrate-like water through direct hydrogen-bonding, positioning and slowing the dynamics of water at the trough of the binding site. We uncover a correlation between slower dynamics of water at the binding site for the protein in solution and stronger free energy of binding of the protein to ice. The synergy between hydrophobic and hydrophilic groups unveiled by this study provides guidance for the design of synthetic ice-binding molecules with enhanced ice nucleation and antifreeze activity.