I think Manning screwed himself when he started worring about the temp a week or 2 before the season ended by playing with a glove.
He needs to play his game. He knows he can throw with a glove if he needs to. He either needs to wear a glove all the time or not play with it when it gets cold. Put a couple hand heater packets in his pockets and keep his hand warm all game. I would hope he has those air activated back warmers taped to his back and shoulder during cold games also.