  Recent years have seen excellent progress in modeling the entrainment of T
$\sim$ $10^4$K atomic gas in galactic winds. However, the entrainment of cool,
dusty T $\sim$ 10-100K molecular gas, which is also observed outflowing at high
velocity, is much less understood. Such gas, which can be $10^5$ times denser
than the hot wind, appears extremely difficult to entrain. We run 3D
wind-tunnel simulations with photoionization self-shielding and evolve thermal
dust sputtering and growth. Unlike almost all such simulations to date, we do
not enforce any artificial temperature floor. We find efficient molecular gas
formation and entrainment, as well as dust survival and growth through
accretion. Key to this success is the formation of large amounts of 10^4K
atomic gas via mixing, which acts as a protective "bubble wrap" and reduces the
cloud overdensity to $\sim$ 100. This can be understood from the ratio of the
mixing to cooling time. Before entrainment, when shear is large, t_mix/t_cool
$\leq$ 1, and gas cannot cool below the "cooling bottleneck" at 5000K. Thus,
the cloud survival criterion is identical to the well-studied purely atomic
case. After entrainment, when shear falls, t_mix/t_cool > 1, and the cloud
becomes multi-phase, with comparable molecular and atomic masses. The broad
temperature PDF, with abundant gas in the formally unstable 50 K < T < 5000 K
range, agrees with previous ISM simulations with driven turbulence and
radiative cooling. Our findings have implications for dusty molecular gas in
stellar and AGN outflows, cluster filaments, "jellyfish" galaxies and AGB
winds.
