Realist
Realistically painted mountains are among the most difficult to paint, primarily because there is intense detail that is required. Because you are painting exactly what you can see, it is sometimes best to take a photograph of the scene you wish to paint. This will essentially freeze the moment in place, giving you plenty of time to study the picture and produce the most realistic painting possible. Excellent examples of realistic mountain paintings can be found in early editions of the National Geographic Magazine, as well as the work of Albert Bierstadt.
Impressionist
Painting mountains in the impressionist style requires much more care than painting in the realist style. The emphasis on painting an impressionist piece is in light and movement. Rather than concentrating on the mountain itself, pay close attention to the way the light projects on the mountain, and the way the light moves throughout the day. Pay careful attention to the movements surrounding the mountain, such as birds, the swaying of trees, motions of rivers or waterfalls.
Cubist
Painting mountains in the cubist style requires that you break down the image into its individual components and show several different viewpoints of the mountain from the same perspective. Think of it this way: Mountains are not perfectly round spheres. They have outcroppings, areas that are clear of trees and deep canyons and ravines. In cubism, you are showing all of these to the viewer. Consider taking photographs of the mountain from north, south, east and west. When this is done, translate all of these into a single view that uses basic colors. For an idea as to how it's done, study Paul Cezanne's "Quarry Bibemus."
Expressionist
The underlying philosophy behind expressionism is the interpretation of a scene through the viewer's emotions. To do this requires particular self-discipline, as you must see what you feel about the mountain and the surrounding terrain and commit that to the canvas. For instance, does the mountain fill you with fear? You might paint it black with menacing clouds surrounding it and dark, creature-infested forests surrounding it. If you are feeling blue, paint it exclusively in blue tones. Likewise, if you feel happy to be in the outdoors while painting the mountain, paint it with bright, airy colors and wide, powerful brushstrokes.