Inspired by the superhydrophobicity of animal and plant surfaces (via the lotus effect and petal effect), two microstructures were prepared on the surface of T2 copper by laser texturing. The two-dimensional and three-dimensional morphologies of the sample surfaces were characterized with a scanning electron microscope and a laser scanning confocal microscope, respectively. Chemical composition, wettability, and delayed icing performance were characterized with energy-dispersive spectroscopy, contact angle measurement, and cryogenic freezing, respectively. The surfaces of the two samples had different closed-pore lattice structures. The maximum static contact angle of water on either surface was 155 without any chemical modification of the surfaces. The two superhydrophobic surfaces with different substrate roughnesses exhibited different adhesion characteristics to water. The icing test showed that both surfaces had a significantly delayed icing effect relative to the untreated sample. Based on the one-dimensional heat transfer model of a water droplet in the icing phase transition, the influence of surface morphology on delayed icing characteristics was analyzed. This work provides a simple and effective method for preparing superhydrophobic copper surfaces and theoretical guidance for anti-icing applications of copper metal in low-temperature environments.