Warning: spoilers ahead for Captain America: Sentinel of Liberty #1!
Following the apparent death of Steve Rogers, Bucky Barnes (aka the Captain America, managing to replace the Star-Spangled Avenger despite lacking the Super-Soldier Serum that gives Steve his enhanced abilities. Now, Captain America: Sentinel of Liberty #1 explicitly confirms how the Winter Soldier is able to keep up with genuine superhumans.
Bucky Barnes has one of the more tragic origins and backstories compared to other superheroes in the Marvel Universe. He was famously once Captain America's sidekick and a member of the Invaders in World War II. But after an accident, Bucky was lost at sea just like Captain America. Except Bucky wasn't found by the Americans like Cap. He was found by the Russians and turned into their Winter Soldier, an assassin who was fitted with a cybernetic arm and periodically woken from cryogenic sleep to go out on missions only he could accomplish.
In Captain America: Sentinel of Liberty #1 by Jackson Lanzing, Collin Kelly, and Carmen Carnero, Bucky and Cap seek to stop a threat to a parade. While searching for the threat, Bucky points out that while Captain America was on ice, his life was defined by decades of going toe to toe with superpowered beings and even gods. The Winter Soldier was frozen between missions, meaning that his life was a near-unending gauntlet of impossible experiences more extreme even than Steve Rogers' long and accomplished career.
This explains how the Winter Soldier is as strong and fit as he is. While he may not have the Super-Soldier Serum in his veins, he spent the prime of his life fighting every kind of super-powered threat, honing himself to operate on their level. He also had no downtime to lose any of those skills. Missions were all he knew. That type of intense lifestyle has made him as capable as any superhero, especially given his childhood with the Invaders saw his training begin incredibly early.
Another benefit of Bucky being the Winter Soldier is that it adds to his reputation. He states that because of what he did during those decades, even ninjas stay away from him, creating a terrifying psychological advantage even Captain America doesn't have. These kinds of interactions have trained Bucky's mind as well as his body. He says that his eyes are always open and scanning for threats, which is especially helpful to Captain America given the mission they are on. While the Winter Soldier may not technically have super powers, it's clear how his past has elevated him to the level where he can fight alongside Captain America.
