how would well would their body acclimate to being thrust into somewhere with extreme weather (such as high mountains, a desert, or deep jungle)?
These places are not created equal. Perhaps more importantly, the acclimatisation issues are not necessarily related to the changeability or kind of climate a traveller is coming from.
With high mountains (defined as >2500m ASL equivalent on Earth), the principle issue is altitude sickness, and acclimatisation to altitude will likely take a few days. Trying to charge off and perform energetic physical exercise at high altitude can kill you, so at least part of the acclimatisation process is not doing anything stupid. Tendency to engage in stupid activities and die of ignorance is common across human cultures.
The NHS says:
- avoid flying directly to areas of high altitude, if possible
- take 2 to 3 days to get used to high altitudes before going above 2,500m
- avoid climbing more than 300m to 500m a day
- have a rest day every 600m to 900m you go up, or rest every 3 to 4 days
- make sure you're drinking enough water
- avoid smoking and alcohol
- avoid strenuous exercise for the first 24 hours
- eat a light but high-calorie diet
Clearly, acclimatisation will depend partially on the person's lifestyle ahead of time, partially on what they're expecting to do when they get to their destination, and partially on whether they can follow basic instructions.
Similarly with very hot climates, failing to take time to acclimatise can kill. This is perhaps more important, as acclimatisation takes a couple of weeks and requires active engagement in the process. The US Army, for example, has an obvious interest in being able to put people into hot places and have them carry heavy things about without keeling over with heatstroke. From this guide:
Generally, about two weeks of daily heat exposure is needed to induce heat acclimatization. Heat acclimatization requires a minimum daily heat exposure of about two hours (can be broken into two 1-hour exposures) combined with physical exercise that requires cardiovascular endurance, (for example, marching or jogging) rather than strength training (pushups and resistance training). Gradually increase the exercise intensity or duration each day. Work up to an appropriate physical training schedule adapted to the required physical activity level for the advanced military training and environment.
Jungles do not necessarily have either of these problems (though consider the existence of cloud forests) and so acclimatisation issues are more about personal discomfort and following advice to stay healthy, rather than dropping dead because you couldn't skip your morning run (though the local wildlife could still make it fatal, but you can't really become acclimatised to being eaten).