Altitude sickness is usually only a minor problem for most people, and most European resorts are too low for it to be a serious issue.
However, if you are unfit or suffer from low blood pressure, you may experience some of the common symptoms related to staying at altitude:
Shortness of breath
These symptoms generally wear off within 48 hours. If not, you should see a doctor. The problem is more common when visiting American resorts. Some are much higher than those in Europe (approaching 3000m, whereas few resorts in Europe are over 2000m) which means that the risk of altitude sickness is much greater. The air pressure at 2900m is 70% of that at sea level - effectively starving your body of a significant amount of oxygen.
Ideally, you should avoid travelling directly to super-high resorts - if visiting Colorado, a night or two in Denver (1600m) might help - but this is not always possible, so it is important to take certain precautions:
Don't over-exert yourself on your first few days
Drink more water than usual and avoid too much salt intake
Reduce alcohol intake - this has a greater effect at altitude
Eat food that is high in carbohydrates: grains, pasta, fruit and vegetables
In case you want to avoid the whole issue, here is a list of the highest American resorts:
Copper Mountain 2960m
Crested Butte 2855m
Mammoth Lakes 2430m*
Park City 2105m
Winter Park 2745m
Jackson Hole 1925m
Lake Tahoe 1890m
* The Main Lodge at Mammoth Mountain is higher, at 2715m.
Experience suggests that problems for lowlanders are most likely in the group of resorts over 2800m, but when picking your resort note that Steamboat is appreciably lower than other Colorado resorts, and Park City is appreciably lower than its Utah neighbour, Snowbird.
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