Originally Posted by Hawkingbird
On the commentary the director said that Zola's experimenting did have something to do with him becoming Winter Soldier...
specifically, they say that they experimented on him with Zola's version of the super-soldier serum. And that's how he ends up surviving the fall.
But that doesn't explain why it makes it better for HYDRA to have been the ones to turn him into the Winter Soldier. In fact, it makes keeping that role for the KGB easier.