Use sticks or some other measuring device like a ruler or tape measure, with short, medium and long moves. Lengths are 3, 5 and 8 inches. Movement is in a straight line. The one exception is movement on roads follows the road. Facing can be changed before and after each move segment. Firing can be done before or after any move segment.
Movement rates clear terrain rough terrain Line infantry 1 medium (5 inches) 1 short (3 inches) Light infantry 2 short (3 and 3 inches) 2 short (3 and 3 inches) Regular cavalry 1 long (8 inches) 1 short (3 inches) Light cavalry 2 medium (5 and 5 inches) 2 short (3 and 3 inches) Foot artillery 1 medium (5 inches) Only on roads
Units must stop when they reach a terrain feature. That ends that move segment even if the unit didn’t move the full segment. If the unit has another move segment it can then move through the terrain feature. All movement that starts in terrain features uses short segments, even if part of the move ends up being outside the feature. Foot artillery can only move through terrain featureson roads.
There could be variations due to terrain type, unit type, presence of some sort of guide with a unit, etc..
Some of my thinking behind this: It's fairly simple, but still flexible. I think it simplifies terrain effects and avoids requiring calculating remaining movement ratesor fractional moves as you move through different terrain, allows light troops to be more flexible and quick in rough terrain or getting around obstacles. Units like regular cavalry can be fast at the expense of maneuverability.