Freezing of water in hydrophilic nanopores (D=1.2 nm) is probed at the microscopic scale using x-ray diffraction, Raman spectroscopy, and molecular simulation. A freezing scenario, which has not been observed previously, is reported; while the pore surface induces orientational order of water in contact with it, water does not crystallize at temperatures as low as 173 K. Crystallization at the surface is suppressed as the number of hydrogen bonds formed is insufficient (even when including hydrogen bonds with the surface), while crystallization in the pore center is hindered as the curvature prevents the formation of a network of tetrahedrally coordinated molecules. This sheds light on the concept of an ubiquitous unfreezable water layer by showing that the latter has a rigid (i.e., glassy) liquidlike structure, but can exhibit orientational order.