The military does use a grid square reference system, Military Grid Reference System (MGRS), and to resolve the issues when sufficiently far north, the grid squ

The military does use a grid square reference system, Military Grid Reference System (MGRS), and to resolve the issues when sufficiently far north, the grid squares stop being aligned with the latitudes and longitudes, but rather just sit lined up with the 0/90/270/180 longitudes, as a sort of circular cap cut out of grid paper. (Properly speaking, it's Universal Transverse Mercator (which is a series of 60 Mercator projections) between 80S and 84N, and Universal Polar Stereographic near the poles).