It has to be nearish vertical (how close depends on energy, but it's a pretty wide band around vertical) so that all of its energy is not absorbed in the atmosphere. As you get closer to horizontal trajectories you go through way more atmosphere. Neutrino-induced cascade would typically be initiated within the ice , not at the surface (in principle they could be at the surface but we would reject them since it's much more likely that it's something else in that case).