Dealing the double-down card face down is one of the oldest of blackjack traditions.
The story goes something like this. Back in the early days, a Horseshoe floor supervisor was watching a game where a player pushed out a double-down bet on his 9-2. Before the dealer put out the double-down card, the boss said, "I’ll bet you your double-down card isn’t a ten-value."
The player replied, "You’re on."
The boss then instructed the dealer to place the DD card face down. Thus, a blackjack tradition was invented.
Today, dealing the DD card face down is due to this tradition. You’re permitted to look at the face-down dealt card, but most players get a thrill out of waiting for the dealer to turn their DD card over. Dealing the double-down card face down doesn’t give the casino any advantage, nor is it used to thwart cheaters. It’s just a way to make the game more exciting. In fact, if you're playing at a casino that deals them up and you'd like to get yours down, the dealer will almost always oblige if you ask.
Specific to your question, while there's no rule that dictates whether the double-down card is dealt face down or up, it's likely to be dealt down in single- and double-deck games where the original two cards are also dealt down and players handle the cards and up in shoe games where the original cards are dealt up and touching the cards is prohibited.
