We present hydrodynamical simulations of galactic winds from star-forming galaxies including nonequilibrium ionization and frequency-dependent radiative transfer, processes that have remained largely unaccounted for in galactic wind studies. We consider radiation from massive stars, the metagalactic UV/X-ray background, and the self-radiation of the supernovae heated gas. We compare our results to classical galactic wind solutions and show the importance of our newly included physical processes toward observations of ions such as O iii, O vi, O vii, and O viii plus the observable soft X-ray spectra. Nonequilibrium ionization is reflected in overionized gas compared to equilibrium solutions, leading to much enhanced column densities of highly ionized species. The wind produces excess soft X-ray (E ≳ 100 eV) radiation that is several orders of magnitude higher compared to the metagalactic background. This radiation ionizes the higher ions (such as O vii) somewhat, but affects the lower ions (such as O iii) significantly. We predict that the observable X-ray spectra should contain the signatures of such nonequilibrium effects, especially in X-ray lines such as O vii and O viii. Simple estimates suggest that both the temperature and density of the winds may be overestimated by factors of a few to almost 2 orders of magnitude using simple equilibrium models. We conclude that both the nonequilibrium ionization and the radiation from the wind itself need to be considered for proper modeling of the optical/UV/X-ray emitting plasma in galactic winds.