A common theme is redemption. Bucky's past as the Winter Soldier is often explored, and the OC plays a role in his journey towards redemption. For example, in many stories, the OC helps him face his past actions and find a way to move forward.
There's also 'Bucky and the Unlikely Companion'. This fanfic shows how an OC, who is a healer, helps Bucky deal with his past traumas. It's a very heartwarming story with some great character development for both the OC and Bucky.
He could interact in a protective way. For example, if it's a small animal like a rabbit, he might build a safe place for it. His military training would make him good at creating a secure environment.
For 'dark winter soldier fanfiction', Falcon could be an interesting character to pair with the Winter Soldier. Falcon has his own set of skills and a strong moral compass. He could help the Winter Soldier navigate the modern world and his newfound freedom. Also, Scarlet Witch would be a fascinating pairing. She could potentially help him deal with his traumatic memories through her powers. And Bucky could also be paired with Doctor Strange. Strange could use his magic to help Bucky understand and control the dark forces within him.