Higher elevation (usually found in mountainous terrain) has several effects. The primary effect on ballistics is that the air density is reduced. Air density is a combination of temperature, pressure, and molecular weight. The latter is mostly a function of humidity. Water is the only molecule which changes abundance in air very much. Water molecules are lighter than oxygen, nitrogen, carbon dioxide or argon in their normal molecular forms, so moist air lowers air density some.
Bullets do drop less with reduced air density. They lose less of their energy so they hit harder. They also have less wind deflection for a given wind speed, and bullets are more stable in lower density air.
However, with increased elevation it's normal to have lower temperatures and in mountainous terrain wind speed are often (but not necessarily) higher then on on lower elevation flat land.
In general high elevation makes a firearm more accurate unless the powder is affected by cold.
Winds may be higher though which can make wind estimation more difficult. In cold mountain air doping wind is very difficult. Mirage and plant movement may not be available and winds around mountains are are quite variable and not only horizontal.
The shooter is also likely to be affected by high elevations. Breathing is more rapid and deeper. Above around 10,000 feet thinking may be impaired, and cold can cause stiff fingers and shivering.
The biggest effect of elevation is if you don't take the changes from lower elevations (where most of the effects of the atmosphere are greater) into account. Nearly any ballistics program will show what the effects reduced air density will be. If you plan a trip for mountain hunting you should make up new range tables. Also check what environment you're going to encounter. Failure to dress properly is likely to be the biggest problem with high altitude hunting.
