"What I'd like to know is if there are extra things to take into account when winter-camping at high altitude?"
Your body's water balance gets all screwed up. You are inhaling cold and dry air, and you are exhaling warm and moist breath, so (1) you are losing energy and (2) you are losing moisture with every breath. If you are lucky and healthy, your body will reach a new water balance point within a couple of days of arriving up there, and then you have a better chance of beating the worst of the high altitude illness problems. Still, it is worthy to consider getting prescription Diamox (acetazolamide).
However, your body will tend to be warm during the day while you are active, and then it cools down at night. As a result, your body's blood volume changes. That is why it is common to feel the need to urinate at night. Due to the extreme cold and elevation, you will find it most practical to use a dedicated pee bottle within the tent. Most climbers using this idea do not want to make the mistake of grabbing the wrong bottle, so they typically decorate it with a Capital P or something unmistakable, along with your initials. Plus, you and your tentmates need to set a protocol for which direction from the tent door is used for gathering clean snow to melt, and which direction is used for dumping the pee bottles.
Anecdote: While climbing a very high peak, these two old guys were sharing a tent, and they knew about the need for a pee bottle, so each had one. On one night, one guy could not find his own pee bottle, so he used the other guy's pee bottle. That brought on the first argument. On the next night, the same guy could not find either pee bottle, so he used the common cook pot. That brought on the ultimate argument.