It spanned the time the Winter Soldier was in Russia, though his main trainer/handler was actually a woman (who eventually married Lukin, if I'm remembering properly). She had frostbite scars on her face from doing sniper work in the winter, and Bucky grew to be both dependent and unfailingly loyal to her. There's a scene toward the end where they stroll arm and arm through a public park in order to meet Alexander Pierce, and she brags to him about having such a deadly weapon under her thumb.
Unfortunately, the name of the character escapes me, as does the title and author of the fic. Can someone hopefully point me in the right direction?