Stellar winds of cool carbon stars enrich the interstellar medium with significant amounts of carbon and dust. We present a study of the influence of two-fluid flow on winds where we add descriptions of frequency-dependent radiative transfer. Our radiation hydrodynamic models in addition include stellar pulsations, grain growth and ablation, gas-to-dust drift using one mean grain size, dust extinction based on both the small particle limit and Mie scattering, and an accurate numerical scheme. We calculate models at high spatial resolution using 1024 gridpoints and solar metallicities at 319 frequencies, and we discern effects of drift by comparing drift models to non-drift models. Our results show differences of up to 1000 per cent in comparison to extant results. Mass-loss rates and wind velocities of drift models are typically, but not always, lower than in non-drift models. Differences are larger when Mie scattering is used instead of the small particle limit. Amongst other properties, the mass-loss rates of the gas and dust, dust-to-gas density ratio, and wind velocity show an exponential dependence on the dust-to-gas speed ratio. Yields of dust in the least massive winds increase by a factor four when drift is used. We find drift velocities in the range 10-67 km/s, which is drastically higher than in our earlier works that use grey radiative transfer. It is necessary to include an estimate of drift velocities to reproduce high yields of dust and low wind velocities.