The Launching of Cold Clouds by Galaxy Outflows III: The Influence of
  Magnetic Fields
  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-Alfv\'enic 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.
