Cold-weather warfare
History: Northern and Eastern Europe were the venues for some well-documented winter campaigns. During World War II several actions took place above the Arctic Circle. Recent cold-weather conflicts have occurred in the Himalayas.

Pre–1800: In 1242, the Teutonic Order lost the Battle on the Ice on Lake Peipus to Novgorod. In 1520, the decisive Battle of Bogesund between Sweden and Denmark occurred on the ice of lake Åsunden.
In 1643 or 1644, Prince Rupert made an abortive attack on the Parliamentarian stronghold of Aylesbury England. 500 men are reported to have frozen to death on 21 January. On 25 January a sudden thaw caused a bridge to collapse over the River Weaver, splitting Royalist cavalry forces at the Battle of Nantwich resulting in their defeat.
The 1557 Siege of Katsurayama was fought between the forces of the Japanese daimyō Takeda Shingen and Uesugi Kenshin as part of the Kawanakajima campaigns. Katsurayama castle was a strategically vital Uesugi stronghold in the contested Shinano Province and, when it was isolated from reinforcements due to late snow in early 1557, the Takeda clan used this opportunity to seize it under Baba Nobuharu, shielded from view by heavy snowfall.
Sweden and Denmark fought several wars during the 16th and 17th centuries. As a great deal of Denmark consists of islands, it was usually safe from invasion, but in January 1658, most of the Danish waters froze. Charles X Gustav of Sweden led his army across the ice of the Belts to besiege Copenhagen. The war ended with the treaty of Roskilde, a treaty very favorable to the Swedish.
During the Great Northern War, Swedish king Charles XII set off to invade Moscow, but was eventually defeated at the Battle of Poltava after being weakened by cold weather and scorched earth tactics. Sweden suffered more casualties during the same war as Carl Gustaf Armfeldt with 6,000 men tried to invade Trondheim.  Three thousand of them died of exposure in the snow during the Carolean Death March.

19th century: During the Finnish War, the Russian army unexpectedly crossed the frozen Gulf of Bothnia from Finland to Åland and, by 19 March 1809, reached the Swedish shore within 70 kilometres (43 mi) from the Swedish capital, Stockholm. This daring maneuvre decided the outcome of the war.
Napoleon's invasion of Russia in 1812 resulted in retreat in the face of winter with the majority of the French army succumbing to frostbite and starvation, rather than combat injuries.
The Battle of Weihaiwei was a battle of the First Sino-Japanese War in the winter of 1895 in Weihai, Shandong, China between the forces of the Japan and Qing China. Through a well coordinated offensive of both naval and land forces, hampered by snow and cold, the Japanese destroyed the forts on shore and sank much of the Chinese fleet.

20th century: 

World War I: During the First World War, soldiers on the Western front involved in trench warfare were forced to deal with freezing conditions, trench foot, frostbite, and disease. The winter of 1916-17 was exceptionally cold, which caused great hardship and deaths among the soldiers. Equipment and vehicles also were not suited for the freezing conditions.
At the Battle of Sarikamish, Ottoman troops were unprepared for winter fighting and suffered major losses, with 25,000 freezing to death before the battle even began.
On the Italian front, fighting bogged down in trench warfare but at mountain elevations. On White Friday, thousands of troops from both sides were killed in avalanches in the Dolomites.

World War II: The Finnish Army used ski troops during the Winter War and the Second World War in which the numerically-superior but road-bound Soviet forces were vulnerable to attack by mobile, white-clad ski troops, approaching from untracked, frozen terrain.
The Wehrmacht maintained elite mountain troops, Gebirgsjäger. They were organized in small, specialized units, which relied on pack animals. Typical weapons were light machine guns, mortars, and anti-tank guns. Control of ridge lines was paramount, using a limited number of outposts. They operated on the principles of fewer arms, but more ammunition per weapon and the economical use thereof.
In Operation Barbarossa in 1941, both Russian and German soldiers had to endure terrible conditions during the Russian winter. The German-Finnish joint offensive against Murmansk (Operation Silver Fox) in 1941 saw heavy fighting in the Arctic environment. Subsequently, the Petsamo-Kirkenes Operation conducted by the Soviet Army against the Wehrmacht in 1944 in northern Finland and Norway drove the Germans out. In late 1944, Finland turned against its former cobelligerents of Nazi Germany under Soviet pressure and pressured the Germans to withdraw in the ensuing Lapland War. While use of ski infantry was common in the Soviet Army, Germany formed only one division for movement on skis.
From June 1942 to August 1943, the United States and Canada fought the Japanese in the Aleutian Islands Campaign in the Alaska Territory.

In the Arctic: The following actions were fought in the Arctic by land and naval forces in World War II between 1941 and 1945 in the following theaters of operations:
Finland – The Winter War was a military conflict between the Soviet Union (USSR) and Finland. It began with a Soviet invasion of Finland on 30 November 1939, three months after the outbreak of World War II, and ended three and a half months later with the Moscow Peace Treaty on 13 March 1940.
In the Battle of Suomussalmi, Finns leveraged cold weather to disadvantage the Soviet enemy troops by targeting field kitchens and campfires for their attacks, thereby denying those troops warmth and nutrition. The Finns rotated their troops so that they could regularly return to warm shelters to recuperate after an attack or patrol. Heavy Soviet equipment and their associated troops were restricted to roads, while Finnish ski troops had broad mobility to outflank the enemy. The threat of Finnish snipers, whom the Russians called "cuckoos", further demoralized the Soviets. The Finns mined ice routes over lakes to sink Soviet equipment.
The Lapland War was fought between Finland and Germany from September 1944 to April 1945 in Finland's northernmost Lapland Province. It included:

Operation Birke (birch) was a German operation late in World War II in Finnish Lapland to protect access to nickel.
Operation Nordlicht (northern lights) was a German scorched-earth retreat operation in Finland during the end of World War II.
The Petsamo–Kirkenes Offensive was a major military offensive during World War II, mounted by the Soviet Army against the Wehrmacht in 1944 in northern Finland and Norway.
Norway – The liberation of Finnmark was a military operation, lasting from 23 October 1944 until 26 April 1945, in which Soviet and Norwegian forces wrestled away control of Finnmark, the northernmost county of Norway, from Germany. It started with a major Soviet offensive that liberated Kirkenes.
Northern Russia – Operation Silver Fox was a joint German–Finnish military operation offensive during World War II. It failed to achieve its main goal to cut off and ultimately capture the key Soviet port at Murmansk through attacks from Finnish and Norwegian territory.
Spitsbergen – Operation Gauntlet was a Combined Operations raid by Canadian troops, with British Army logistics support and Free Norwegian Forces servicemen on the Norwegian island of Spitsbergen, 600 miles (970 km) south of the North Pole, from 25 August to 3 September 1941. Operation Fritham was a Norwegian military operation, based from British soil, that had the goal of securing the rich coal mines on the island of Spitsbergen (a part of Svalbard) and denying their use to Nazi Germany. Operation Zitronella (Citronella) was an eight-hour German raid on Spitzbergen on 8 September 1943. This marks the highest latitude at which a land battle has ever been fought. However, given the extreme conditions, the German and Allied troops were at times compelled to assist each other to survive.
United States – The Aleutian Islands Campaign was a campaign conducted by both the United States and Imperial Japan from 3 June 1942 to 15 August 1943 in Attu and Kiska, part of the Aleutian Islands in Alaska during World War II.

Post World War II: The Battle of Chosin Reservoir was a stark example of cold affecting military operations in the Korean War. There were many cold injuries and malfunctions of materiel, both vehicles and weapons.
The Sino-Indian War was a Himalayan border conflict between China and India that occurred in 1962. India initiated a Forward Policy in which it placed outposts along the border in 1961.  China launched simultaneous offensives in Ladakh and across the McMahon Line on 20 October 1962. Chinese troops advanced over Indian forces in both theaters. Much of the fighting took place in harsh mountain conditions, entailing large-scale combat at altitudes of over 4,000 metres (14,000 feet). Many troops on both sides succumbed to the freezing cold temperatures.