Motivated by observations of outflowing galaxies, we investigate the combined impact of magnetic fields and radiative cooling on the evolution of cold clouds embedded in a hot wind. We perform a collection of three-dimensional adaptive mesh refinement, magnetohydrodynamical simulations that span two resolutions, and include fields that are aligned and transverse to the oncoming, super-Alfvenic material. Aligned fields have little impact on the overall lifetime of the clouds over the non-magnetized case, although they do increase the mixing between the wind and cloud material by a factor of $approx 3.$ Transverse fields lead to magnetic draping, which isolates the clouds, but they also squeeze material in the direction perpendicular to the field lines, which leads to rapid mass loss. A resolution study suggests that the magnetized simulations have somewhat better convergence properties than non-magnetized simulations, and that a resolution of 64 zones per cloud radius is sufficient to accurately describe these interactions. We conclude that the combined effects of radiative cooling and magnetic fields are dependent on field orientation, but are unlikely to enhance cloud lifetimes beyond the effect of radiative cooling alone.
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