I think extending the line that runs from Orion's sword (the Orion Nebula) to the middle belt star (Alnilam) to the horizon to find north only works when the Orion constellation is near overhead. This applies to our equatorial regions. Otherwise, when Orion is for example near the horizon, extending the line points in the northern direction but it would run parallel to the horizon and not down to the horizon at due North.
Better to use the two Big Dipper stars (extending from Merak to Dubhe), when visible, to run a line down to the horizon at due North (again, equatorial regions only). This works at all times that these two stars are above the horizon.