We present hydrostatic equilibrium models of spherical, self-gravitating clouds of helium and molecular hydrogen, focusing on the cold, high-density regime where solid- or liquid-hydrogen can form. The resulting structures have masses from 0.1 Msun down to several x 1.e-8 Msun, and span a broad range of radii: 1.e-4 < R(AU) < 1.e7. Our models are fully convective, but all have a two-zone character with the majority of the mass in a small, condensate-free core, surrounded by a colder envelope

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... re phase equilibrium obtains. Convection in the envelope is unusual in that it is driven by a mean-molecular-weight inversion, rather than by an entropy gradient. In fact the entropy gradient is itself inverted, leading to the surprising result that envelope convection transports heat inwards. In turn that permits the outer layers to maintain steady state temperatures below the cosmic microwave background. Amongst our hydrostatic equilibria we identify thermal equilibria appropriate to the Galaxy, in which radiative cooling from H2 is balanced by cosmic-ray heating. These equilibria are all thermally unstable, albeit with very long thermal timescales in some cases. The specific luminosities of all our models are very low, and they therefore describe a type of baryonic dark matter. Consequently such clouds are thermally fragile: when placed in a harsh radiation field they will be unable to cool effectively and disruption will ensue as heat input drives a secular expansion. Disrupting clouds should leave trails of gas and H2 dust in their wake, which might make them easier to detect. Our models may be relevant to the cometary globules in the Helix Nebula, and the G2 cloud orbiting Sgr A*.