Crystallographic textures are presented of ice formed in situ by directional cooling of saturated porous rocks. The observations of texture demonstrate that pore invasion, and not repeated nucleation, dominates the freezing process in these rocks. This implies that microscopic advance of crystallographically coherent ice occurs through the pore network. The textures are governed by the permeability of the pore network and not by the direction of bulk heat flow. The anisotropy of permeability provides a mechanism for grain competition during ice growth, as crystals with fast growth directions aligned favorably to the maximum permeability are favored.