We study the effects of drag on an idealized relativistic MHD wind of radial geometry. The astrophysical motivation is to understand the effects of radiation drag on the dynamics of a jet or wind passing through the intense radiation field of an accreting compact object. From a critical point analysis, we find that a slow magnetosonic point can appear in a dragged flow even in the absence of gravitational force, as a result of a balance between the drag force and the combination of thermal pressure and centrifugal forces. As in the undragged case, the Alfven point does not impose any constraints on the flow. Although it is formally possible for a dragged flow to possess more than one fast magnetosonic point, we show that this is unlikely in practice. In the limit of a "cold," centrifugally driven flow, we show that the fast magnetosonic point moves to infinite radius, just as in the drag-free case. For a given mass flux, the total energy output carried to infinity, and the final partition between the kinetic energy and the Poynting flux, are the same for the dragged and the drag-free flows. The main effects of radiation drag are to increase the amount of energy and angular momentum extracted from the source and to redistribute the regions where acceleration occurs in the flow. This is accomplished through the storage and release of magnetic energy, as a result of additional winding and compression of the field caused by the action of the drag. For a relativistic wind, the dissipated energy can exceed the final kinetic energy of the flow and may be comparable to the total flow energy (which is dominated by Poynting flux). The energy lost to radiation drag will appear as a Doppler-boosted beam of scattered radiation, which could dominate the background radiation if the flow is well-collimated.
