The Orlesian warden is not involved in this quest to search the cure
The Orlesian Warden is not mentioned. Not the same thing. Since, indeed, Bioware's writers have no reason to make their own job harder by splitting the lore, the more likely outcome is that when the cure quest is mentioned again in a future instalment, it will be stated in worldstates with the Orlesian Warden that s/he went to look for a cure, same as he surviving HoFs: makes everything easier.
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The Orlesian Warden has no ties to Leliana (or any of the DAO LIs) therefore, there's no one at Skyhold who would know how to get in touch with him or her.
Also, unlike the HoF, the Orlesian Commander wasn't on top of Justinia's short list for the job of Inquisitor.
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I'd prefer to play a warden in a story focused around whatever is happening in Weisshaupt than shoehorn it into a tevinter/Qunari story.
Seconded: I hope things don't get Wardeny at all in DA4: let's focus on the Tevinter-Qunari arc and bring back the Wardens when the next Blight begins (because, come on! unless the series is cancelled before its conclusion, we all know there will be another Blight before the grand finale)
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If we ever play that Grey Warden Civil War Arc it would I assume take place before trespassers
If I were a betting man, I'd put money on the Wardens' inner-conflict arc beginning after the conclusion of DA4, with the gap between the conclusion of Inquisition and the beginning of that arc being justified by saying that the Warden's conflict was until then more akin to a cold war that's just about to heat up. Hawke is then out of the picture, back in Kirkwall chilling with Varric, Aveline & co and his/her involvement can be kept as a secondary part of the backstory mentioned only in codex entries and a couple of dialogues and banters.