Stellar winds of cool and pulsating asymptotic giant branch (AGB) stars enrich the interstellar medium with large amounts of processed elements and various types of dust. We present the first study on the influence of gas-to-dust drift on ab initio simulations of stellar winds of M-type stars driven by radiation pressure on forsterite particles. Our study is based on our radiation hydrodynamic model code T-800 that includes frequency-dependent radiative transfer, dust extinction based on Mie scattering, grain growth and ablation, gas-to-dust drift using one mean grain size, a piston that simulates stellar pulsations, and an accurate high spatial resolution numerical scheme. To enable this study, we calculated new gas opacities based on the EXOMOL database, and we extended the model code to handle the formation of minerals that may form in M-type stars. We determine the effects of drift by comparing drift models to our new and extant non-drift models. Three out of four new drift models show high drift velocities, 87–310 km s−1. Our new drift model mass-loss rates are 1.7–13 per cent of the corresponding values of our non-drift models, but compared to the results of two extant non-drift models that use the same stellar parameters, these same values are 0.33–1.5 per cent. Meanwhile, a comparison of other properties such as the expansion velocity and grain size show similar values. Our results, which are based on single-component forsterite particles, show that the inclusion of gas-to-drift is of fundamental importance in stellar wind models driven by such transparent grains. Assuming that the drift velocity is insignificant, properties such as the mass-loss rate may be off from more realistic values by a factor of 50 or more.