[en] The dynamics of colliding-wind binary (CWB) systems and conditions for efficient particle acceleration therein have attracted multiple numerical studies in recent years. These numerical models seek an explanation of the thermal and nonthermal emission of these systems as seen by observations. In the nonthermal regime, radio and X-ray emission is observed for several of these CWBs, while gamma-ray emission has so far only been found in η Carinae and possibly in WR 11. Energetic electrons are deemed responsible for a large fraction of the observed high-energy photons in these systems. Only in the gamma-ray regime might there be, depending on the properties of the stars, a significant contribution of emission from neutral pion decay. Thus, studying the emission from CWBs requires detailed models of the acceleration and propagation of energetic electrons. This in turn requires a detailed understanding of the magnetic field, which will affect not only the energy losses of the electrons but also, in the case of synchrotron emission, the directional dependence of the emissivity. In this study we investigate magnetohydrodynamic simulations of different CWB systems with magnetic fields that are strong enough to have a significant effect on the winds. Such strong fields require a detailed treatment of the near-star wind acceleration zone. We show the implementation of such simulations and discuss results that demonstrate the effect of the magnetic field on the structure of the wind collision region.