Water was investigated on a h-BN/Rh(111) nanomesh template using variable temperature scanning tunneling microscopy (STM) and density functional theory (DFT) calculations. Below 52 K, two distinct phases self-assemble within the 3.2 nm unit cell of the nanomesh that consists of "holes" and "wires". In the 2 nm holes, an ordered phase of nano-ice crystals with about 40 molecules is found. The ice crystals arrange in a bilayer honeycomb lattice, where hydrogen atoms of the lower layer point to the substrate. The phase on the 1 nm wires is a low density gas phase. Tunneling barrier height dI/dz spectroscopy measurements reveal the dipoles of individual molecules in the nano-ice clusters and access proton disorder.