Fighting a war in the mountains can be vastly different than fighting a war in a jungle. Some of the principles remain the same, like superior firepower, maneuvering into advantageous positions, and securing your resources, but the terrain and geography an Army fights in can dictate how a leader goes about establishing and maintaining certain advantages during battle. Modern war is still subject to the rules of terrain and geography, as some units learned in a very costly way in Afghanistan.
Historically, it was easier for Armies to fight in open fields and on relatively forgiving terrain. Many battles were fought in fields, valleys or similar areas of easily used terrain. It made sense for both sides to desire a fight in easy terrain. Massive overgrowth could impede the use of arrows and the movement of other troops. Mountains and hills make it difficult to fight, even for both sides. Unless there is a secured mountain pass or some sort of ad-hoc fortification built, both sides will be struggling going up and down the terrain as they fight. Deserts are extremely hostile to large armies, and not only is it difficult to find water, the dust takes a toll on visibility and the physical capabilities of soldiers.
Marching an Army through the Alps and bringing war elephants with, was truly the feat of an amazing general and leader.
Unfortunately for soldiers and commanders on campaign, they often have to move through these difficult areas, if not outright fight in them. While they may eventually fight in a field, or a lush valley, soldiers would have to endure days, weeks, or months on end of marching through the jungle, or hiking up and down the mountains. Sometimes they would be harrassed by patrols of enemy troops, seeking to demoralize them and sap their enemy’s strength.
Hannibal Barca, the Carthaginian General that wreaked havoc on the Roman Republic, marched through the Alps to descend on Italy. While marching through the Alps, he suffered massive losses to his Army and War elephants (some estimate it was up to 50%), but he still made it through to the other side and was able to campaign and fight battles in the much less harsh terrain of central Italy (among other places). Alexander the Great faced a huge terrain disadvantage when he mounted the siege on Tyre, but he found a workaround to the coastal island’s favorable terrain and sacked Tyre. The Romans struggled to extend rule to the dense forests of Germania and the harsh environs of the Northern British Isles.
During war, hostilities can erupt in the most unfavorable conditions and terrain, and it is the job of the leaders in the Army to ensure their troops are ready to fight in whatever challenging terrain may present itself. Armies can march through the mountains, and tanks can move through dense forests… These sorts of movements through harsh terrain have allowed attacking armies to utilize terrain to their advantage. The Germans moved through the Ardennes forest to attack France, and to initiate the Battle of The Bulge. Guerrillas in the Afghan mountains resisted Soviet and American forces for well over two decades.
France developed a massive series of fortifications thinking the Germans would not be able to effectively move through the Ardennes forest.
As a commander, it is important to understand the effects of the environment one will fight in. It is unrealistic to expect every unit and every soldier to be specialists in all types of warfare, but a cursory knowledge of mountain warfare, and a basic understanding of jungle fighting can go a long way for a conventional unit. Rudimentary skills that are taught and drilled develop even more so if a unit goes and fights in new terrain. A unit with a basic understanding in mountain warfare, desert warfare and jungle warfare will come back from a deployment to the mountains with a thorough and sometimes expert understanding of mountain warfare. By teaching the troops the basics of fighting in each terrain, commanders and leaders set their units up for success, while allowing them to develop their skills if they ever deploy to a certain area.
Currently, the United States military is in the process of aligning their brigades toward geographic regions. This seems to be a good idea, but overspecialization of a unit as large as a Brigade (5,000 troops or more) can be dangerous. If multiple brigades were required to deploy to a certain geographic region, or move through a region they are unfamiliar with, their readiness and warfighting ability would be compromised. Terrain is an equalizer, and fortunately for those studying war, it changes very slowly (it takes tens of thousands of years for terrain and geology to change noticeably). Due to this, leaders can prioritize the importance of different terrain types, while still maintaining basic readiness in all areas.
History is filled with countless examples of wily soldiers and leaders using terrain to their advantage to tip the side of a battle or campaign. Relying on terrain to win the war though, usually does not work out, it simply delays the inevitable. But a general that understands a heavily defended mountain pass can choke an army with superior numbers (like Leonidas did to the Persians), or a Sergeant that understands a patrol base set up in an open valley is likely to be attacked, can use their knowledge and experience in terrain to outmaneuver enemies and bring more firepower to bear down on the enemy. Moving through harsh terrain quickly can guarantee you arrive earlier, with more time to prepare defenses, rest your troops and begin an assault.
It gets cold in Russia; failing to understand and plan for this basic fact was one of the reasons the Wehrmacht was doomed in Russia.
Modern military planners almost seem to discount terrain entirely. Sending heavily, mechanized brigades to fight mobile wars in Afghanistan, or relying on trucks in a Russian winter that have no anti-freeze to deliver critical supplies, is a failure of military leaders to understand terrain and the effects terrain can have on troops and equipment. Technology and training can take the bite out of operating in hostile terrain, but the mountains, jungles, deserts and arctic environs will always have their say.