Prevention of ice crystallization is a challenging problem with implications in diverse applications, as well as examining the fundamental low temperature physics of water. Here, we demonstrate a simple route, inspired by water confinement in antifreeze proteins, to inhibit crystallization and provide high water mobility of highly supercooled water using supramolecular hydrogels of copolymers of dimethylacrylamide (DMA) and 2-(N-ethylperfluoro octane sulfonamido)ethyl acrylate (FOSA). These hydrogels can suppress or inhibit freezing of their water, depending on the copolymer composition. Dynamic and static neutron scattering indicate that hydrogels using the copolymer with 22 mol % FOSA partially inhibit ice formation. This behavior is attributed to confinement (<2 nm) of water between the hydrophobic FOSA nanodomains that prevents 45% of the water within the hydrogel from freezing even at 205 K. Very fast dynamics of the amorphous water are observed at 220 K with an effective local diffusivity decreased by only a factor of 2 from that observed at 295 K within the hydrogel using the copolymer with 22 mol % FOSA. The spacing between the hydrophobic nanodomains, tuned through the copolymer composition, appears to modulate the water that can crystallize. These fully hydrated hydrogels (at equilibrium with liquid water at 295 K) can enable a significant fraction of highly supercooled water to be stable down to at least 205 K.