Gorshkov was born on 20 September 1902 on the "khutor" of Olshanka, Don Host Oblast. During the Russian Civil War, the area was occupied by the Armed Forces of South Russia until August 1919, and Gorshkov remained engaged in agricultural work. Conscripted into the Red Army in September 1920, he was sent to study at the 7th Borisoglebsk Cavalry Course. With a cadet detachment drawn from the course, Gorshkov fought in the suppression of the Tambov Rebellion as a squad leader. For his actions in the fighting, he was awarded the Order of the Red Banner.