If everone folds their hand in Texas hold'em and the winning player voluntarily shows one of his cards does he have to show the other card?

You are allowed to protect your cards with your hands in any game of Poker however you must ensure that your cards are visible to the dealer and all other players at the table to ensure they know you are in the hand.

Depending on the houserules of the casino/homegame your hand might be folded if you "hide" your cards from the other players/dealer.