Can a player look at face-down cards in exile that they own but didn't exile themselves?

Face-down cards in exile are hidden by default. CR 406.3 states that players may look at face-down cards in exile only if a spell, ability, or rule specifically allows it. Ownership alone does not grant that permission — there is no general rule letting you peek at your own face-down exiled cards.

In practice, effects that create face-down exiled cards often include their own look-permission. For example, Morph and Manifest cards that get exiled face-down via certain effects may carry wording like "you may look at this card at any time." If that permission is absent from the exiling effect, no player may look at the card without a separate enabling effect.

The fact that you own the card is irrelevant under the rules. CR 400.2 notes that a card's owner does not have special access rights to its hidden information unless a rule or effect grants it. Similarly, it doesn't matter whether you were the one who exiled it — what matters is whether the applicable spell or ability granted look-access.

Concrete example: Suppose your opponent uses Gonti, Lord of Luxury to exile a card from your library face-down. Gonti's ability grants your opponent (not you) the right to look at and potentially cast that card. You, as the owner, cannot look at it — the effect specifically granted the permission to the controller of Gonti, not the card's owner.

If you ever encounter a face-down exiled card with no associated permission text, no player may look at it (CR 406.3). When it eventually leaves exile or the effect ends, it is turned face up at that time.