Hiking 3 quarters triggers an endurance roll for forced march, fail that and you don't progress plus 1 agility damage. Hiking all 4 quarters is an even more difficult endurance roll, plus at least one of those quarters is certainly at night and you'll have skipped sleep as well.
Even mounted I'd apply the same but when you're mounted you'll also have to make an animal handling check for your horse or risk it going lame. I would also houserule that generally travelling mounted is no faster than on foot, trying to go the faster rate should automatically count as a forced march for your animal.
You also may want to require an additional water consumable roll maybe even two if its summer if you're going into forced march territory.