Mountain warfare, in land combat, can encompass a wide range of techniques. At the most basic, infantry may need to carry their own supplies, because the trails are too narrow for vehicles. There not even be trails, and, while it is a specialized qualification, skilled soldiers may be able to move vertically, using ropes and technical rock climbing equipment.
High mountains may call for skills in arctic warfare, as a mountain rising from a jungle can still become very, very cold.
As air pressure drops with altitude, equipment may work differently, or refuse to work. Helicopters lose power with decreasing air density. Projectiles fired from artillery and mortars, used in indirect fire will have different trajectories than in thicker air.