I didn't see the game - my interest was purely baseball at the time.
From my understanding, one of the reasons the Bengals won was psychological: The Chargers are from a sunnier environment. When they saw some Bengals players show up in short sleeves, they felt they had lost the game.
"I'll never forget the cold that day. I can still feel it," former Bengals linebacker Reggie Williams, who also went bare-armed, told the Boston Globe's Jim McCabe. "It was so cold that day we didn't bother with the pregame warmups, but when we came out for the game and saw the Chargers, we could see it in their faces. They had just a little glimmer of false hope and we knew it was over. They saw us bare-armed; the intimidation factor had worked. It was worth it, from that standpoint."