The metal arm is powerful, dexterous to a point, but there is a reason he often leads with using his right arm in an attack unless he needs that sheer strength for defence or attack. It puts him at a slight disadvantage to have to favour it.

Not as much of a disadvantage as he, belatedly, realises his footing presents him. Snow, ice and water are pretty much the worst combination to be on, especially with a taller heavier opponent bearing down on him. So Bucky strikes out with the machete, taking his only chance to plant his feet and hope for the best, he knows he weighs no insignificant amount with muscle and metal but that metal also makes him heavier on one side. It's a toss up as to whether Thor's charge or Bucky's footing will win out.

The machete's blade cuts towards Thor's chest at the moment the Asgardian's arm comes down with the knife at Bucky, the knife's blade scraping along the metal with a terribly high screech of sound. Then in the next moment the bigger man impacts with Bucky and Bucky -- Bucky slips.

He goes down and maybe Thor goes down with him, tumbling and rolling backwards to the outer ice of the lake's surface. Bucky reaches out with his right, hand, forgetting his injury as he scrabbles for purchase. He feels the wound tear itself open anew and start to soak the bandage with blood, leaving a messy streak on the ice. It's hard to tell if his own strike injured Thor in the moment.