  The molecular phase of supernova-driven outflows originates from the cold,
molecular gas in the disc of a star-forming galaxy, and may carry a substantial
fraction of the wind mass flux in some galaxies, but it remains poorly
understood. Observations of this phase come mostly from very nearby galaxies
due its low surface brightness and covering fraction, and simulations often
lack the spatial resolution necessary to resolve it. Here we analytically
estimate the survivability of this phase in order to understand under what
conditions an galactic wind can contain a significant molecular phase. We show
that the molecular content of outflows is primarily determined by two
dimensionless numbers: a generalised Eddington ratio describing the strength of
the outflow and an ionisation parameter-like quantity describing the strength
of the radiation field per baryon. We apply this model to a sample of galaxies
and show that, while any molecules entrained in the winds of normal
star-forming galaxies should be destroyed close to the galactic disc, the
outflows of strong starburst should become increasingly dominated by molecules.
