Gorshenin was born in Vladivostok, Russia, the fourth child and eldest son of five children from Nickolai Gorshenin, who was a Colonel in the Imperial Russian Army, and Anastasia Gorshenin (née Branski). The family became separated in the chaos after the fall of Vladivostok, the last city to hold out from the Bolshevik revolution. His mother had to trek the harsh Siberian landscape, with her two young daughters and one week old baby Nick, to Harbin to meet up with her husband.