We present calculations for a magnetized hybrid wind model for asymptotic giant branch (AGB) stars. The model incorporates a canonical Weber-Davis (WD) stellar wind with dust grains in the envelope of an AGB star. The resulting hybrid picture preserves traits of both types of winds. It is seen that this combination requires that the dust parameter (Γd) be less than unity in order to achieve an outflow. The emergence of critical points in the wind changes the nature of the dust-driven outflow; simultaneously, the presence of a dust condensation radius changes the morphology of the magnetohydrodynamic (MHD) solutions for the wind. In this context, we additionally investigate the effect of having magnetic-cold spots on the equator of an AGB star and its implications for dust formation, which are seen to be consistent with previous findings.