The Seebeck coefficient and electrical resistance of Bi1-xSbx nanowire arrays electrodeposited in etched ion-track membranes have been investigated as a function of wire diameter (40-750 nm) and composition (0 <= x <= 1). The experimental data reveal a non-monotonic dependence between thermopower and wire diameter for three different compositions. Thus, the thermopower values decrease with decreasing wire diameter, exhibiting a minimum around similar to 60 nm. This non-monotonic dependence of the Seebeck coefficient is attributed to the interplay of surface and bulk states. On the one hand, the metallic properties of the surface states can contribute to decreasing the thermopower of the nanostructure with increasing surface-to-volume ratio. On the other hand, for wires thinner than similar to 60 nm, the relative increase of the thermopower can be tentatively attributed to the presence of quantum-size effects on both surface and bulk states. These measurements contribute to a better understanding of the interplay between bulk and surface states in nanostructures, and indicate that the decrease of Seebeck coefficient with decreasing diameter caused by the presence of surfaces states can possibly be overcome for even thinner nanowires.