NPCs to use exactly same movement rules as player character.

[PALU]

My experience is that enemies tire out eventually, but some can run quite far before it starts to affect them. I've attributed that to a light load. Note that "quite far" may well be sufficient for them to catch up with you, in which case you'll have to chose whether to fight back or continue to try to get away (fighting is definitely tiring).

If there is a thick crust on the snow it's probably faster to run than to ski on it, but running will tire you out eventually, while skiing will not (in these conditions, at least if you're a skilled skier).

[Homocommando]

It's not hard to imagine strikes going downwards have more impact than those going upwards, considering existence of the gravity. Upwards attacks also should be considered more tiring. Might be less visible for stab attacks while for slashes it will be clear, though all the small things make a difference.

I am pretty sure that has mostly to do with ergonomics, not gravity. You can slash much faster, with much faster acceleration than just dropping a sword. And I wouldn't say someone standing lower immediately means all your attacks have +9.8m/s² acceleration, while his get -9.8m/s².

Although with heavier two handed weapons it would probably start getting more significant.

By my bruises given and received. Some of us, like myself, have been re-enactors doing high impact sports... like armored combat and I don't mean tanks.

But you are not usually reenacting duels, with one of the combatants standing uphill, right? I can agree high ground gives you an advantage in group combat, but I don't see how it helps you in a duel. (And that was the original point, player fighting an NPC.) Especially when you are standing so much higher... In the discussed scenario, when NPC has their shoulders at the height of the player's ankles, assuming both parties are armed with a sword NPC can hit player's ankles while being ~1,5 meters away, while player would barely be able to even reach the raft he's standing on with his sword.

Battle of Hastings... the Saxons were all fine until they came off the high ground. The fate of Angleland was all down hill from there. yuk yuk yuk.

But that wasn't because they came off the high ground, rather because they ignored their orders, broke their formation and chased after the "retreating" enemy. And again, this is group combat.

It is probably mentioned by many pre-gunpowder era warfare texts. There is also a detailed Wikipedia article on this matter, here:
https://en.wikipedia.org/wiki/High_ground

This is about large scale group combat as well.
AND including cavalry and archers... And for those units high ground definitely matters more... It's harder and less effective to charge uphill, projectiles are affected by gravity for a longer period, so gravity affects their range more. Also if the enemy is above you, fortifications make it much harder to shoot them. If they are below you, fortifications provide cover only to those immediately in front of them.

So yeah it definitely matters, but without cavalry, without archers, it matters less. In a duel I am not sure if it matters, and I definitely wouldn't want to engage alone someone who's standing so much below me his head is at my ankle level.