The techniques you typically use at lower altitude will work fine up there as well. 12.000 feet is in fact not all that high all things considered.
Be careful with the usage of PL filter, overdoing it can result in virtually black skies if the air is clear. I typically don't use PL much in Alpine environment unless a particular cloud situation makes it worth having very dark skies. Under-exposed skies are likely to exhibit some form of posterization that is a pain to get rid of.
One thing you should be aware of is that there is good chance of suffering from some sort of altitude sickness if you go high by car, since the rate of climbing is much higher than when hiking. Unless you have a good physical condition (ability to run 30 minutes without feeling a particular exhaustion) and no particular weakness to altitude, you are very likely to feel tired as soon as you walk around a little, especially if you carry gear.
This has also the potential to reduce your mental sharpness a little bit, which can result in some stupid mistakes you would normally not do (like forgetting to double check the focus, or getting some blown highlights).
This will only be worsened if the temperature is below what you are used to at lower altitudes. Taking a warm shoes, a very warm hat and a good glove system (2 layers) are 2 important aspects when shooting in cold weather. Drinking a lot is also important since the air will typically be extremely dry.
If you are not used to shooting under stress, with the duty to succeed and no other chance to get that one shot, you should also anticipate the fact that this stress could reduce your ability to take the right decisions. A bit like that super important exam that you fear.
Considering all these things, my number #1 advice would therefore be to focus on taking a few images well, instead of snapping around like crazy. If you have 2 hours on the spot, I would shoot for something like 20 images at most, but 20 "perfect" images.