When a large amount of water is deposited onto a bare h-BN/Rh(111) nanomesh, the formation of ordered and stable nano-ice crystals in the pores has been experimentally observed. The present work proposes different possible models for the structure of the observed clusters, based on density functional theory calculations of two-dimensional water lattices adsorbed on free-standing hexagonal BN. Through the investigation of the electronic properties, the interaction with BN, and the distribution of the molecular dipoles, the most probable two-dimensional arrangement has been identified. Finally, a model is proposed for the nano-ice cluster trapped in the pore of the nanomesh, which constitutes 38 molecules distributed according to the most probable two-dimensional arrangement on free-standing BN. Structural and electronic properties of the optimized nano-ice cluster are also reported, and it is shown that the model is consistent with the experimental observation.