Security footage from Howard Stark's death in Captain America: The Winter Soldier that Hydra's super-assassin was the one responsible, with Marvel ultimately confirming that Bucky Barnes was transformed into the Winter Soldier following his presumed death in 1945.
After dancing around Howard and Maria Stark's deaths, Captain America: Civil War explicitly showed the assassination. Part of Baron Zemo's plan to split the Avengers apart included showing the footage to Tony. The security camera caught the car crash and Winter Soldier shooting Howard, but also an intriguing audio detail. Winter Soldier is unmasked during the mission and Howard recognizes Bucky, calling him Sergeant Barnes. At that point, Winter Soldier's identity was not widely known, so how did Howard know it was Bucky?
Both of them have roles in Captain America: The First Avenger, but Howard and Bucky never shared the screen. Thankfully, there are several easy explanations for how Howard would recognize Sergeant Barnes. Stark worked at the SSR base during World War II and operated closely with Captain America. It would stand to reason that Howard and Bucky would've crossed paths at some point. Howard even remarks in The First Avenger that one of his jobs was outfitting Captain America and his men, which inevitably would lead to him meeting Bucky.
There are other ways that Howard would recognize Bucky, even if they didn't meet during WWII. Following Bucky's death and his heroics with Captain America and the fellow Howling Commandos, a memorial site for them was set up in the Smithsonian Air and Space Museum in Washington DC. Bucky's face was prominently featured there, but he was also featured in footage from the time used in a documentary. This all points to the fact that Bucky Barnes would be a known person, so Howard may very well simply recognize him from his role in America's - and Captain America's - history.
Although Howard might have recognized Bucky as the man behind the Winter Soldier identity, the rest of the world didn't figure out who he was until much later. Steve only learned of Bucky's true fate and The Falcon and The Winter Soldier, and hopefully it sets up a promising MCU future for Bucky.
