O chapéu de galinha aparece quando você morre muito, e o jogo pergunta se você quer diminuir a dificuldade. Mas daí o chapéu serve apenas pra indicar que o jogador optou por essa dificuldade, com os soldados mais "cegos" e tal.
Although seemingly a joke, the Chicken Hat actually serves a specific purpose. Kotaku reports that frequent failure or difficulty with missions will cause the game to ask players if they'd like to wear the hat. When selected, a hat appears on the in-game character, who then becomes nearly invisible to all surrounding enemies.
Essentially, it's designed to act as an aid to help players through tougher sections of the game.
http://www.ign.com/articles/2014/12/27/kojima-reveals-chicken-hat-in-metal-gear-solid-5-the-phantom-pain