We investigate by first-principles pseudopotential calculations the structural properties and the energetics of undoped and Si-doped unpassivated GaAs nanowires (NWs). On the basis of total energy calculations for the undoped NWs as a function of diameter we find that, in contrast to the bulk phase, wurtzite (WZ) NWs are more stable than zincblende (ZB) NWs for diameters up to about 50 Angstrom. We also investigate the preferential position of Si dopants in GaAs WZ NWs: we find that donors segregate to the surface, while acceptors prefer inner positions. On the basis of the formation energy study, the stability ranges for Si donor and acceptor sites are similar to the bulk ZB case, with a slight increase in the stability range for donor sites. However, in contrast to acceptors, donors preferentially segregate to surface dangling-bond sites at large NW diameters, and act as deep impurities, rather than shallow donors, thus hindering n-type conductivity. This could contribute to explain the preferential p-type behavior which was observed in recent experiments on Si-doped NWs grown by molecular-beam epitaxy, in addition to other possible effects, including, e.g., the kinetics of Si incorporation.