Adventuring is tiring work, when you think about it. Traveling across wilderness after wasteland, slay beast foul and fantastic, saving the helpless and carting their lazy buts back to civilization, not to mention the loot. How can one forget the loot?! And it's not like it doesn't show up in the fiction either, I mean, dealing with being tired from walking is most of the page count of lord of the rings after all.
But DnD and its ilk rarely have a good mechanic for this, or rather, not very usable ones. 3e had a pile of conditions, including fatigue and exhaustion that I'd always forget, and 5e has a downward spiral of exhaustion that I'd rather not remember, one that is so punishing that I can't hit the players with it too often or they'll not want to adventure at all. Besides, I usually play Knave, or my co-writers variant Brave, most of the time these days.
Furthermore, I find using exhaustion as a side mechanic rather redundant anyway. DnD since it's creation has had a baked in mechanic for indication how much fight a PC has in them before they need to lay down and rest- hit points. Using HP to measure a character's actual physical integrity makes less and less sense the more you think about it, it's more of a mechanic to measure how long you can keep on fighting- so why only make it decreased by attacks?
So yeah, have exhaustion effects deal damage, simple enough, barely a rule hack at all, in knave I'd go with d8 damage (a hit die) every time a character would get tired by something, perhaps with a constitution save. In 5e I'd double it- 2d8- still based on an average hit die, befitting warriors more than mages, in Od&d it would need to be a d6, since all HD are d6. Really base the damage on the system- more modern systems making retrieving hp easier so go for more punishing effects, and save for half rather than save for no damage.
So that"s all well and good, but when do characters get tired? To answer that I refer to some advise from Gygax in the 1e adnd dm guide:
YOU CANNOT HAVE A MEANINGFUL CAMPAIGN IF STRICT TIME RECORDS ARE NOT KEPT.
Now, I'm kinda loosey goosey at the best of times, but this is important, often times if there isn't an explicit ticking clock players always seem perfectly willing to ignore time entirely like they are playing a videogame- the 15 minute adventuring day is a well known issue. And a big problem with that is you do need some sort of penalty for characters faffing about, and this can help, along with wandering monsters. So I propose a regular interval for checking your exhaustion- one that can be modified by other factors- difficult terrain, bad weather, sickness and poison.
Now, the most common time intervals I've seen in games are thus: 24 hours, 8 hours, 1 hour, 10 minutes (a dungeon turn-you could switch this to twelve minutes since it makes that math easier) 1 minute and a combat round (six seconds usually). If you are lounging around town it would only crop up if you are partying for twenty four hours nonstop, but traveling I'd set it at every eight hours. Then each factor would move it to the next interval, from 8 hours to one hour, to every ten minutes, then to each minute and then each round. Now if you are using hexes, or any other abstract way to cut your movement into manageable pieces, I'd just add the damage together for a single roll per hex- and definitely only save for half- players should thing twice before running their characters into the ground.
So what are our factors? Moving at a higher speed (lets say double to make the math easy and memorable) is one. Cold or hot weather is another. Difficult terrain slows characters down anyway so I wouldn't have woodlands or hills be a factor, but I'd definitely have swamps and mountains. If a character is sick or poisoned that's gonna factor. Swimming is absolutely a factor, as is being overburdened. So while traveling at a steady pace on flat land you'd only check once every 8 hours, climbing a snowy mountain forces a check every ten minutes- unless you have cold weather gear- which removes the cold factor. Other things could benefit this as well, like hearty meals instead of iron rations, or magic for that matter. Suddenly, players will be traveling like people, not like horses in skyrim. (also having a mount to get tired for you and cover ground faster is suddenly a more attractive option too).
Now, there should be another twist- if you get into a random encounter while traveling you make you're next exhaustion check at the beginning of the encounter, just to make them scarier and make player's less relaxed about fighting their one random encounter of the day. This won't be needed in dungeons as you won't be travelling and a dungeon should have threats enough as it is, unless of course the dungeon is a particularly tiring one like a natural cave system, a lava fortress or ice castle, or worse yet, Ice caves.
The last thing I have to address is whether or not this is too punishing at low levels- and in knave I'd have to concede it might be, especially if the players rolled poorly on HP- we don't really want them dying on the way to the dungeon, that's what the first room is for. So here's two options- exhaustion cannot reduce your to lower than 1 hp, or if you are using the starvation rules from Veins of the Earth like I do, move down the starvation track. This is a bigger issue with hirelings and companions, so I recommend that if they are going to fall from exhaustion, instead of taking damage their morale is reduced by one, with one point of morale being healed with their HP from rest.
I think this add-on brings a lot to the table, especially if you are going to have wilderness adventure and travel as a part of your game. It helps ensure that keeping track of time means something without having to add a story reason to keep focused. It makes finding easier paths a real concern, rather than just trying to power your way through a straight line. And it makes a big delicious meal taste as good as treasure.