Characters travelling off-road, through difficult terrain and conditions may at the Referee’s discretion face a Natural Lore skill test, to maintain the normal movement rate. If they fail cut the daily move by half. If they fumble they face some sort of danger as determined by the Referee, a dangerous animal or an environmental hazard, or simply are lost and make no progress that day.
If you are using the Encumbrance rules characters who are overloaded, move at half that amount.
Referees may optionally make a fatigue test if the terrain or conditions were particularly taxing. For example, if the characters travel along a well-maintained road with places to stop and rest, with food and water, then there is no need to make a test, while at the other end of the spectrum if the characters were hiking through rough hilly terrain with no comfort breaks under a particularly harsh sun the Referee can call for a Hard (-20%) or even Impossible (-50%) fatigue test at the end of the day’s travel.
If you need to determine which of two groups of comparable movement rate reached a destination first, precisely, use an opposed Athletics (for walking characters) or Riding test (for mounted characters).