Another question, if my opponent Swords to plowshares my Watcher for tomorrow in resp to his Hideaway ability, i'll search for a card in the top 4 of my library which will stay exiled face-down forever ?
1) No. A face down card in exile has no characteristics. Even if you know what it is, it is still face down so it doesn't have the ability to be cast from exile.
2) Yes, the ability still resolve as normal. So you would likely be better off exiling a land or something you don't care about.
In the case of exiling Misthollow Griffin face down due to hideaway, the face-down card does have a characteristic, namely the ability "The player who controls the permanent that exiled this card may look at this card in the exile zone", but notably, that card generally has no other characteristics, including the ability "You may cast Misthollow Griffin from exile" (C.R. 406.3a, 702.75a, 109.3; under C.R. 101.1, hideaway overrides C.R. 406.3a in part; see also this thread), so if Misthollow Griffin was exiled face down due to hideaway, it normally can't be cast from exile.
EDIT (Feb. 17, 2020): See comment 6.
EDIT (Feb. 4, 2021): Edited to conform to rule update for Kaldheim.
EDIT (Feb. 11, 2022): One rule was renumbered in the meantime.
EDIT (May 3, 2022): Edited to conform to rule update for Streets of New Capenna.
After rereading the rules, I was wrong in part. Even on June 6, 2019, when the War of the Spark version of the rules were in effect, what was then C.R. 406.3 read in part: "Unless [a face-down card in exile] is being cast face down ..., the card is turned face up just before the player announces that they are playing the card", and this is still the case as of Theros Beyond Death (see what is now C.R. 406.3a). Thus, if you own Misthollow Griffin face down in exile, and at least if you're otherwise allowed to look at that card, you may still begin to cast that card face up. As part of doing so, you turn the card face up before announcing you will cast that card from exile. This conclusion is reinforced by C.R. 601.3e, a rule added in Throne of Eldraine.
EDIT (Feb. 4, 2021): Moreover, this didn't change with the release of Kaldheim, which added C.R. 406.3b, a rule that does not cover this situation since it applies only if a spell or ability "allow(s) a player to cast spells with certain qualities from among face–down cards in exile", which is not the case with hideaway.
EDIT (Feb. 11, 2022; Mar. 5, 2022): With the release of Kamigawa: Neon Dynasty, C.R. 406.3 now allows a player "instructed to look at a card and then exile it face down", as with hideaway (C.R. 702.75a), to "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". Thus, if a player exiles Misthollow Griffin face down due to hideaway, that player may in any case cast that card face up due to C.R. 406.3a.
EDIT (May 3, 2022): With the release of Streets of New Capenna, the ability the card exiled with hideaway gains changed from "Any player who has controlled the permanent that exiled this card may look at this card in the exile zone" to "The player who controls the permanent..." (C.R. 702.75a). Thus, in general, a player is allowed to look at that card in exile only if—
that player currently controls the "permanent that exiled th[at] card", or
that player exiled that card due to hideaway (see C.R. 406.3).
Let's admit i control a Food chain, a Birds of paradise without summonning sickness and i cast a Watcher for tomorrow which finds me a Misthollow griffin in the top 4 cards and exile it face-down when ETB with Hideaway.
I tap Birds of paradise for U, then exile it with Food chain for UUmanas, and then use a land. I got UUU1. Can i cast the Misthollow griffin exiled face-down with the Watcher for tomorrow with my mana ?
Another question, if my opponent Swords to plowshares my Watcher for tomorrow in resp to his Hideaway ability, i'll search for a card in the top 4 of my library which will stay exiled face-down forever ?
Thank you !
2) Yes, the ability still resolve as normal. So you would likely be better off exiling a land or something you don't care about.
, so if Misthollow Griffin was exiled face down due to hideaway, it normally can't be cast from exile.EDIT (Feb. 17, 2020): See comment 6.
EDIT (Feb. 4, 2021): Edited to conform to rule update for Kaldheim.
EDIT (Feb. 11, 2022): One rule was renumbered in the meantime.
EDIT (May 3, 2022): Edited to conform to rule update for Streets of New Capenna.
EDIT (Feb. 4, 2021): Moreover, this didn't change with the release of Kaldheim, which added C.R. 406.3b, a rule that does not cover this situation since it applies only if a spell or ability "allow(s) a player to cast spells with certain qualities from among face–down cards in exile", which is not the case with hideaway.
EDIT (Feb. 11, 2022; Mar. 5, 2022): With the release of Kamigawa: Neon Dynasty, C.R. 406.3 now allows a player "instructed to look at a card and then exile it face down", as with hideaway (C.R. 702.75a), to "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". Thus, if a player exiles Misthollow Griffin face down due to hideaway, that player may in any case cast that card face up due to C.R. 406.3a.
EDIT (May 3, 2022): With the release of Streets of New Capenna, the ability the card exiled with hideaway gains changed from "Any player who has controlled the permanent that exiled this card may look at this card in the exile zone" to "The player who controls the permanent..." (C.R. 702.75a). Thus, in general, a player is allowed to look at that card in exile only if—