Remember one of the dialogues between you and Solas is:
"For what it's worth, thanks for the castle."
"For what it's worth, you used it well."
Before I played Trespasser my Lavellan Inquisitor was getting quite attached to Skyhold. It was the first place he'd lived in for any length of time and the place he associated with his love, Dorian. However, now it feels tainted and in any case is miles from where he needs to be. May be they'll keep it as a sort of sanctuary or just abandon it but he's heading north to his new base in Kirkwall, helpfully provided by Varric, before checking up on his clan in Wycombe, because they at least need to know about the Dread Wolf and what he proposes to do. He's hoping that they can then pass on the information to other clans; don't believe Fen'Harel, we were entirely right about him, he's not to be trusted. Whether it will get through to them or not is another matter.
The only reason I can think for keeping a force in occupation at Skyhold is that since this was probably the place where he originally formed the Veil, may be he will have to return there as his jumping off point for removing it.