He was picked for Operation Winter Soldier to carry out particular activities in US-controlled West Berlin because he passed as an American soldier and the Soviets intended to deploy an American weapon against the US. When it became clear that Bucky was actually a Russian agent, Zola killed him.
Zola was a codename used by the CIA during the Cold War to identify agents who could be trusted with highly classified information. They used many people with different codes names including Joe, Tom, Charlie et al.
It is possible that Zola was also an alias used by another agent who had recruited Buck before he joined the agency.
There is some evidence that supports this theory. In The Man From U.N.C.L.E. episode "The Secret Weapon" (1966), a Soviet agent named GRADY is sent to Europe with a new invention called a "neutron bomb". When U.N.C.L.E.'s Elizabeth Clayton meets with GRADY, she asks him what his code name is. He replies "Zola", which you can see on her file.
Director Nick Fury acknowledges the existence of the Winter Soldier, and Steve discovers proof that the assassin is actually Bucky, who is still alive but brainwashed and unable to recall his true identity. Captain America puts the Cosmic Cube on the Winter Soldier after defeating him, stating, "Remember who you are." Cap then joins the other Avengers as they face off against Iron Man in New York City.
Winter Soldier makes his debut in The Avengers (2012). He is portrayed by SONYA FIALKOVSKY.
Although he does not appear in the film, Bucky's presence is felt throughout through the use of a flash-back scene that shows how he survived World War II. In this scene, we see Steve Rogers (CAPTAIN AMERICA) being tested by Doctor Boromir (THE LADY VENGEANCE) for his role as Commander of the American Army. After passing the test, Steve agrees to become the new Captain America. However, while watching his friends be killed before his eyes, Steve realizes what kind of life this would be and decides not to go through with it. He breaks his glass mask and leaves the room, only to be confronted by Bucky, who has just been freed from his brainwashing.
When Bucky assassinated the Winter Soldier in Captain America: Civil War, Howard Stark recognized him, and here's how he knew. During the mission, the Winter Soldier is unmasked, and Howard recognizes Bucky as Sergeant Barnes. Later on, after Steve has been frozen in ice for 70 years, Bucky comes to see him at his California home. When asked by Stark if he knows why someone would do this, Bucky only replies with "Yes". This indicates that both men know each other from somewhere, probably during World War II when both served under Colonel Steve Rogers (who was then known as Captain America).
However, it could also be possible that Howard just assumes that Bucky is his son because they look similar.
The Winter Soldier (James Buchanan "Bucky" Barnes) is a hero-turned-villain-turned-hero-again in the Marvel Universe, as well as Captain America's former sidekick. He first appeared in Tales of Suspense #39 (March 1964).
Bucky has been called both a hero and a villain throughout his history. However, whatever action he takes is always for the good of humanity; whether that be saving the President from assassination, stopping nuclear war, or freeing prisoners from prison camps, Bucky is always ready to fight for what he believes in. Although he was given orders to kill Steve Rogers at one point, he instead saved him. This showed that even though Bucky may seem like a villain at times, he actually cares about those around him.
After being brainwashed by HYDRA into killing Captain America, Bucky then decided to turn evil all together and start a new life under the name The Winter Soldier. This angered Captain America who then sent him off to live with Mr. Abraham Lincoln Van Cleef where he raised him up to be a hero again. After hearing about the current crisis that our world is in, Bucky decides to go back in time and stop Hitler from becoming leader of Germany. This causes an explosion which kills Bucky but gives Steve Rogers a new body so he can continue on as Captain America.
Despite his personal objective to eliminate the world of superhumans, Zemo informed Bucky that he had chosen not to murder the Winter Soldier, but Bucky did not look willing to return the favor at first. He pressed the trigger on a revolver aimed at Zemo's head, and it clicked. Bucky then realized he was locked in a battle with his former partner and friend and ran away. Later, after Zemo had been defeated, Bucky returned to face him again.
He shot Zemo in the chest, but it had no effect. Frustrated, Bucky grabbed hold of the barrel of the gun and pulled it out of its holster. Seeing this, Zemo laughed evilly and said: "You can't escape me, Barnes. I'm everywhere, even in death." At that moment, an electric shock jolted through Bucky's body and he fell to the ground unconscious.
When he came to, Zemo was gone but there were several guards standing over him. One of them kicked Bucky in the back of the head and he woke up to find himself imprisoned once more inside the military prison called The Tomb. This time, however, there was no one left to free him.
Some time later, Zemo visited Bucky in his cell. He told him that he had decided not to kill him after all and offered him a job.