Recently, superhydrophobic materials with photothermal and electrothermal conversion functions have received much attention in solving icing problems. However, the currently emerging methods still suffer from the complexity of the preparation method, poor hydrophobicity, or poor abrasion resistance. Herein, a robust copper oxide layer with a high-low staggered structure was prepared on the polymer surface by laser-induced selective metallization (LISM), which can be used for anti-icing and all-day (daytime and night) de-icing. The high-low staggered structure of the superhydrophobic copper oxide surface gives the surface excellent hydrophobicity, light trapping capability, and high electrical resistance, resulting in the surface with superior delayed icing, photothermal de-icing, and electrothermal de-icing capabilities. The copper oxide layer has a water contact angle (CA) of up to 161.3° and a surface delayed icing time of 1374 s, which is 8.23 times longer than the conventional copper layer prepared by LISM. In addition, the surface temperatures of the copper oxide layer are 67.6 °C and 57.3 °C, respectively, under 1.0 sun irradiation or at 5 V applied voltage. Under these conditions, the copper oxide surface’s photothermal and electrothermal de-icing times are 159 and 186 s. In addition, the high-low staggered structure of the prepared superhydrophobic copper oxide surface makes the surface less susceptible to abrasion, resulting in excellent mechanical robustness of the copper oxide layer surface. The proposed method is suitable for low-cost large-scale manufacturing, which guides the preparation of copper oxide superhydrophobic materials for anti-icing and all-day de-icing, and has good application prospects.