The majority of the Feuerberg campaign takes place on, in and between, two mountains which are approximately the height of Mount Everest in our world. Altitude is therefore a recurrent concern. I want some simple rules to cover dealing with it that won't turn into a lot of minutiae.
The key information to know for these rules is that the campaign area is split into three altitude regions: the base of the two mountains, their faces, and their summits. And one can be either unacclimatised or acclimatised to each region.
The base is anything below about 4km in vertical height from sea level. That's the town of Hoch, the valley between the mountains, and about the first 2km onto either mountain (you start about 2km up already). All PCs begin acclimatised to this height, and do not lose their acclimatisation to it.
The Faces of the Mountains
The faces are the portions of either mountain between 4km and 8km vertical height from sea level. This is a true montane environment, and the altitude at which people begin to run the risk of fatal complications. All PCs begin unacclimatised to it.
While they are unacclimatised, they must make a saving throw at the end of each day that they have engaged in strenuous activity. Failure means they lose 1d4 HP and cannot regain hit points, as hypoxia and altitude sickness rip up their metabolism. Days spent resting do not require one to make a saving throw.
Characters who have acclimatised to the face stay acclimatised so long as they don't descend below the face. There are no negative consequences once one has acclimatised.
The Summits of the Mountains
The summit is anything above 8km in vertical height from sea level. Feuerberg gets close to 9km high, even with the top of it shorn away, and its summit area is about 3km in diameter. Himmelberg is about 8.5km high, with a much smaller summit of only 1km diameter. In real life, we call these places "death zones", and they lack enough oxygen to sustain human life for more than a few hours.
Regardless of how acclimatised or unacclimatised one is, one cannot digest food, can't sleep, and must make a saving throw every hour or lose 1d4 HP while in the death zone.
Unacclimatised characters on the summit must also make a separate saving throw every hour or begin dying when they're in the summit. It takes 1d6 turns to die, through a combination of hypoxia, cerebral edema, pulmonary edema, and cold.
Acclimatised characters don't have to make the saving throw to avoid dying. Character stay acclimatised to the summit only so long as they don't descend from the summit.
So being unacclimatised is pretty bad. You probably want your PC to acclimatise to the altitude they're going to. Here are some methods for doing so.
Any spell that provides you with breathable air of some sort (e.g. a spell for travelling underwater or the void) will provide you with suitable air to count as acclimatised for as long as it lasts. Magic items that provide similar capabilities will also work, as do weird mutations and magical powers you get from mystery cults. If the magic lapses or the item ceases function, you count as unacclimatised and start suffering the consequences within 1 turn.
2) Camping and waiting
The most accessible method. You camp in a hex adjacent to the region you want to become acclimatised (i.e. on a base hex adjacent to the face to become acclimatised for the face, on a face hex adjacent to the summit for the summit, etc.). For the face, you camp for two weeks, for the summit, a month. At the end of that time, you roll a saving throw and if you succeed, you are now acclimatised until you next descend the mountain. You can repeat the period of waiting and camping as many times as one wants, in case not everyone passes the first time, but once acclimatised, you don't need to roll a saving throw again. You get random encounters while you camp, so you're going to either want a fortified camp or to find ways around having to do this.
3) Eating weird stuff
At the start of the Feuerberg campaign, you can't buy anything that will let you acclimatise more easily or rapidly. But, there are several options that you can go hunt down on the mountain itself to make acclimatisation either easier or faster. These are the ones that are openly known, though few have ever seen or used them.
Fresh Yeti Spleen - A yeti's spleen can be split between 1d4 people. It grants acclimatisation to the altitudes of the faces for 1d4 days for each person who eats it. The yeti strenuously object to this practice (-4 to positive reaction rolls), can smell spleen-eaters from far away, and do their best to make life difficult.
Blue Coca - A blue-green plant that grows wild in montane climates, where its fragrance is precious to minor air elementals, who drape themselves in smells the way mortals do clothes. A small amount is cultivated as a recreational drug by the Xarxeans, though they don't make it available to humans. Chewing quids regularly (for at least a week straight, 8 hours a day) before an expedition means it will only take a day to become acclimatised to the face, and three days for the summit. You can't heal naturally (only from medical care) while chewing blue coca.
Grey Mantaka - A psychedelic drug of unknown origin, though rumours claim a particular monolith high on Himmelberg oozes the stuff on nights of the new moon. Grey Mantaka acclimatises you to both the face and summit immediately upon taking it, for 1d6 days each. You must also make a saving throw or hallucinate wildly. This means you fail all saving throws to disbelieve illusions, suffer a -2 on attack rolls, and concentrating on anything for more than a minute or so requires a roll of 5+.
Other drugs and concoctions are rumoured to exist, but knowledge of their existence must be sought out in play.