Metal surface oxidation is governed by surface mass transport processes. Realistic surfaces have many defects such as step edges, which often dictate the oxide growth dynamics and result in novel oxide nanostructures. Here we present a comprehensive and systematic study of the oxidation of stepped (100), (110) and (111) Cu surfaces using a multiscale approach employing density functional theory (DFT) and reactive force field molecular dynamics (MD) simulations. We show that the early stages of oxidation of these stepped surfaces can be qualitatively understood from the potential energy surface of single oxygen adatoms, namely, adsorption energies and Ehrlich-Schwöbel barriers. These DFT predictions are then validated using classical MD simulations with a newly optimized ReaxFF force field. In turn, we show that the DFT results can be explained using a simple bond-counting argument that makes our results general and transferable to other metal surfaces.