The origin for the Winter Soldier is VERY similar to the comics, but with notable differences:
-Bucky is recovered by the Russians, not Zola or the Germans. Also, Bucky was thought to have "died" in the same plane explosion that Captain America was on. They had both successfully got on the drone plane to try and diffuse Zemo's bomb (in the comics, Cap is fighting Baron Zemo during WW2). Main difference was that Bucky was thought to have been dead for years and Cap is famously frozen in a block of ice. Turns out the freezing waters also preserved Bucky and he is recovered (with a missing arm) by a Russian sub. In the movies, he "dies" during the train mission and earlier than he does in the comics.
-The Soviet experiment on him, attach a metal arm and "program" him to be a Soviet assassin. He is constantly brought in and out of cryogenic status for missions by the Soviets, hence how he keeps his youth and only ages a few years when Cap meets him in modern times. This is hinted in the movie when they say he's been around like a "ghost" and has committed assassinations for the past 50 years or so. Also, the dossier photo that Cap sees at the end shows Bucky in a what appears to be a frozen state. In the comics, he even has a romantic relationship with the Black Widow (who later on hangs out with him a lot after he recovers his memories) and we see hints in the movie that Widow knows more about the Winter Soldier when she was a KGB agent.
-Winter Soldier becomes a "tool" of former Soviet General Aleksander Lukin (who is later possessed by the Red Skull) similar to the Soldier being a "tool" of Alexander Pierce in the movie.
-Cap uses the Cosmic cube (Tesseract in the movies) to help Bucky recover his memories.
-He basically looks the same in the comics, biggest difference is that instead of eye-goggles and mouthpiece mask, he just wears the standard mask around the eyes. This is probably why we saw Stan's Winter Soldier with the black make-up on in some filming shots as the look was intended to replicate the "eye-mask" from the comics. Obviously, it didn't make the final cut or the make-up was digitally edited out of most of the scenes.
So overall, the character translated VERY well from the comics and his origin is largely in-tact with mostly differences in the characters involved.