The organization that created the Winter Soldier was Hydra. In the Marvel Cinematic Universe, Hydra transformed Bucky Barnes into its most famous brainwashed assassin after he was presumed dead during World War II.
Hydra scientists and handlers used advanced medical procedures, cybernetic enhancements, repeated conditioning, and memory suppression to control Barnes. He was kept in suspended animation between missions, allowing the organization to deploy him across decades while preserving his physical condition.
The program was connected to Hydra's long-term infiltration of S.H.I.E.L.D. and governments around the world. In Captain America: The Winter Soldier, Hydra operative Vasily Karpov oversees the Winter Soldier Program, while Barnes is repeatedly revived and sent on covert assassinations, including the killing of Howard and Maria Stark.
A common mix-up is confusing Hydra with S.H.I.E.L.D. or its tactical unit S.T.R.I.K.E. Hydra secretly infiltrated S.H.I.E.L.D., and some S.T.R.I.K.E. agents were Hydra operatives, but Hydra was the organization behind the Winter Soldier program.