Trying to see what older cards interact w/ a face-down, not yet in the game creatures. First I was thinking Riftsweeper, but that's face-up.
To hone in my research, what zone would a card w/ foretell be in when it's placed face down? Or is it just in limbo such as cards that have been phased out.
Is it considered exiled? And when should it be countered: when it's place faced down or when the rest of it's cost is played? I think the core question is when the foretell cost is initially played, how can the owner of the card or the opponent interact with it?
The mechanics article for Kaldheim has much of your answer.
It notes that if a card with foretell (such as Augury Raven) is in your hand, you may exile it face down by paying 2, not its foretell cost. Thus, the card will be in exile (and not, say, on the battlefield face down) for the purposes of effects that care about exiled cards or cards in exile. (Presumably, the action of exiling the card this way is a special action. Exiling the card this way is not the same as casting the card, though, so it doesn't go on the stack first — compare with All Hallow's Eve [C.R. 108.1].) However, casting the card on a later turn after it's exiled this way is the same as casting any other spell except the foretell cost is paid rather than the mana cost; and the resulting spell can be countered like any other spell.
However, the mechanics article describes the foretell ability rather informally. You will have to wait until the comprehensive rules update for Kaldheim for a more rigorous answer.