Hawkeye and The Winter Soldier have crossed paths with each other over the years.
First Time- 1996
The first time Hawkeye and Winter Soldier cross paths is when Clint is 17 and has left the circus and has been a mercenary for a year.
The Soldier is assigned to take out a politician at a Gala. As The Soldier sets himself in position, he hears a slight ruffle and sees that 20 feet from his perch another sniper is taking his position.
The Soldier observes the other sniper who looks like he is a teenager. The weapon is odd, its a bow and arrow. The trajectory of his shot is bad and it makes the shot near impossible. But when the arrow is released, it hits the target right in his chest. The Soldier watches in admiration. After the target is dead the other sniper packs his equipment and leaves.
The Soldier watches as he disappears and turns to see that his mark has had arrived. The Soldier quickly assassinated the mark and left all the while thinking of the young assassin with a bow and arrow.
Second Time-1998
The second time Hawkeye and Winter Soldier cross paths is when Clint has been a Shield agent for 1year.
Clint Barton has been an Shield agent for a year. He has been assigned to take out an Arms dealer in Kazakhstan. He is preparing to take the shot, when suddenly his target is dead, bleeding on the floor from a bullet hole in the center of his forehead.
Clint looks in the direction that the shot came from, and sees the glint of the mental.
Clint's sharp eyes tell him that the other sniper has a metal arm with a star on it, he is dressed in all black and a mask covers the lower part of his face.
Clint sighs and tells his handler that the target is dead. As he watches the other sniper leave, Clint vows to find out about him.
Third Time-2014
The third time Hawkeye and Winter Soldier cross paths, they meet as Clint Barton and Bucky Barnes.
Its been 3 months since since Bucky was rescued and now he was meeting the other Avengers. He already knew Steve, Natasha, Tony and Bruce. The one's he did not know were Thor and Hawkeye.
Thor was on Asgard so he would have to meet him later. He was curious about Hawkeye though. Steve told him Hawkeye's real name was Clint Barton and that he used bow and arrows.
Hearing that Bucky's mind flashed back to an encounter he had with a teenager who used the same weapons and made an impossible shot.
" Hi I am Clint." said a voice. Bucky turned and his eyes widened. Clint Barton was the same teenager he encountered all those years ago, he just looked older now but Bucky was sure he could still make impossible shots.
Bucky smiled, " I am Bucky, its nice to meet you. I am looking forward to getting to know you well."
Clint's eyes twinkled and he smiled.