Copper foam is widely used in industrial catalysis, flow boiling, and latent heat storage systems. It is expected that a multi-level topology copper foam with micro/nanostructures can further enhance performance. In this study, an electrochemically patterned copper foam with micro/nanostructures was fabricated and used to reduce supercooling in water-based cool storage phase-change materials. By controlling the reaction time (e.g., 195 s, 255 s, and 300 s), the pattern on the copper foam skeleton appeared as granular, dendritic, and coral-like structures, respectively. Compared with a blank group with supercooling of 11 °C during the solidification process, the unmodified copper foam (CF#0s) can reduce it to 7.7 °C. Electrodeposition-patterned copper foam with micro/nanostructures can further reduce supercooling. The average supercooling degree for CF#195s, CF#255s, and CF#300s was further reduced to 5.6 °C, 4.8 °C, and 4.6 °C, respectively. Among them, CF#300s reduced the supercooling and delay time by 60%. This occurred because the micro-nanostructure on the skeleton of copper foam provides abundant nucleation sites for the solidification of water, and surface roughness increases the nucleation rate.