Short answers, pulled from the story.
The winter campaign of 1941-1942 ran from the 5th of December 1941 to the 7th of May 1942. Soviet military command applied that name to the entire period of counter-offensives that followed the German invasion, Operation Barbarossa.
The Moscow Strategic Offensive Operation, launched on the 5th of December 1941, opened the winter campaign. It ran through the 7th of January 1942 and was accompanied almost simultaneously by the Kerch-Feodosia Amphibious Operation, which began on the 25th of December 1941.
Soviet forces recaptured Tikhvin, Klin, and Rostov in December 1941 during the early phase of the winter campaign. These were among the most significant sites regained as the Red Army pushed German forces back.
Although the Red Army forced German units to retreat and recaptured important sites, it mostly failed to encircle the German formations it drove back. German commanders managed to avoid significant casualties even while giving ground, preserving their fighting strength.
The winter campaign comprised more than ten distinct named operations. These included the Lyuban, Demyansk, Orel-Bolkhov, Rzhev-Vyazma, Barvenkovo-Lozovaya, Crimean, and Bolkhov Offensive Operations, among others, running from December 1941 through May 1942.
The Rzhev-Vyazma Strategic Offensive Operation was one of the major Soviet operations in central European Russia, running from the 8th of January 1942 to the 20th of April 1942. It should not be confused with Operation Mars, which refers to a separate Soviet operation in the same area conducted during November and December 1942.