Substitutional group III and group V elements, though commonly used as shallow dopants in bulk silicon, have a limited efficiency in silicon nanocrystals. In this work, we use first-principles models of 1.5 nm nanocrystals with hydride- and silanol-terminated surfaces to understand how oxidation influences the segregation and deactivation of dopants at the surface and the dopant binding energies. We show that the surface oxygen layer changes drastically the radial dependence of the dopant formation energy both for donors and for acceptors, but that, independently from the oxidation, dopant diffusion does not take place at operating conditions. Additionally, we show that the oxidation increases the electron binding energy of the P, As, and Sb and decreases the hole binding energy of B, Al, Ga, and In.