We present numerical magnetohydrodynamic simulations of the effect of stellar dipole magnetic fields on line-driven wind outflows from hot, luminous stars. Unlike previous fixed-field analyses, the simulations here take full account of the dynamical competition between field and flow, and thus apply to a full range of magnetic field strength, and within both closed and open magnetic topologies. A key result is that the overall degree to which the wind is influenced by the field depends largely on a single, dimensionless, ‘wind magnetic confinement parameter’, η* = B
∞, which characterizes the ratio between magnetic field energy density and kinetic energy density of the wind. For weak confinement η* ≤ 1, the field is fully opened by the wind outflow, but nonetheless for confinements as small as η* = 1/10 can have a significant back-influence in enhancing the density and reducing the flow speed near the magnetic equator. For stronger confinement η* > 1, the magnetic field remains closed over a limited range of latitude and height about the equatorial surface, but eventually is opened into a nearly radial configuration at large radii. Within closed loops, the flow is channeled toward loop tops into shock collisions that are strong enough to produce hard X-rays, with the stagnated material then pulled by gravity back onto the star in quite complex and variable inflow patterns. Within open field flow, the equatorial channeling leads to oblique shocks that are again strong enough to produce X-rays, and also lead to a thin, dense, slowly outflowing ‘disk’ at the magnetic equator. The polar flow is characterized by a faster-than-radial expansion that is more gradual than anticipated in previous 1d flow-tube analyses, and leads to a much more modest increase in terminal speed (< 30%), consistent with observational constraints. Overall, the results here provide a dynamical groundwork for interpreting many types of observations, e.g., UV line-profile variability; red-shifted absorption or emission features; enhanced density-squared emission; and X-ray emission, that might be associated with perturbation of hot-star winds by surface magnetic fields.