EDIT: I posted the question on BGG here and game designer Eduardo Baraf has clarified. Discards are face up and both piles can be reviewed by either player at any time.
A discard pile is almost always face up. (this is based my own experience over last 15 years so so of attending UK based games clubs and conventions)
If a discard pile was face down then you run the risk of a player drawing a card from discard pile by mistake. If a discard pile was meant to be face down and its contents secret I would expect this to be specified by that games rules
However, there is an argument that Skulk Hollow should be played with a face down discard even though this isn't explicitly stated.
The Prepare action allows a player to discard a card a draw two cards. It might be the intention to not let your opponent know what card you discarded. Also the recall ability says:-
A hero unit with the RECALL ability may spend one power to allow the
hero player to examine the contents of their discard pile, choose one
card, and return it to their hand.
Even though the rules don't explicitly state you may not examine your discard pile this ability explicit states you may when taking that action. You could infer from that that normally you would not be able to.
The difficulty here is the the rules are not specific about this. Personally I would play with a face up discard as that's what I'm used to in other games but in your situation I would suggest agreeing with who you were playing against first how you play it.