We consider the surface melting of metal nanowires by solving a phenomenological two-parabola Landau model and by conducting molecular dynamics simulations of nickel and aluminum nanowires. The model suggests that surface melting will precede bulk melting when the melt completely wets the surface and the wire is sufficiently thick, as is the case for planar surfaces and sufficiently large nanoparticles. Surface melting does not occur if the melt partially wets or does not wet the surface. We test this model, which assumes that the surface energies of the wire are isotropic, using molecular dynamics simulations. For nickel, we observe the onset of anisotropic surface melting associated with each of the two surface facets present, but this gives way to uniform surface melting and the solid melts radially until the solid core eventually breaks up. For aluminum, while we observe complete surface melting of one facet, the lowest energy surface remains partially dry even up to the point where the melt completely penetrates the solid core.