Once you look at the exiled face-down card once, you may look at it again any time you wish.
Edited Camille POTTIER (May 17, 2019 02:38:32 PM)
406.3. Exiled cards are, by default, kept face up and may be examined by any player at any time. Cards “exiled face down” can’t be examined by any player except when instructions allow it. However, once a player is allowed to look at a card exiled face down, that player may continue to look at that card as long as it remains exiled, even if the instruction allowing the player to do so no longer applies. A card exiled face down has no characteristics, but the spell or ability that exiled it may allow it to be played from exile. Unless that card is being cast face down (see rule 707.4), the card is turned face up just before the player announces that they are playing the card (see rule 601.2).[/quote[
Also keep in mind that we have the following Gatherer ruling for players who are curious and don't know the Comp Rules:Once you look at the exiled face-down card once, you may look at it again any time you wish.
Thanks,
Nathan Long
Magic Rules NetRep