The dungeon at Haven would have survived, being underground, and it may well be that the initial meeting took place there as it was on route out of the Frostback Mountains on the Ferelden side. I imagine the team would have returned to Skyhold to at least remove those things that hadn't accompanied them to the Winter Palace and escort the residents of the tented village (that you can see down in the valley) to a safer place. Since many of them would have been either families of soldiers or pilgrims to Skyhold, they might well wish to return to Haven as a starting point.
However, my Inquisitor would not keep it as a base of operations, particularly with a disbanded Inquisition as they would have no reason to stay in that part of Thedas and it is clear they anticipate future action being in the north. My personal preference would be my new estate that Varric gifted me in Kirkwall. Solas would have no knowledge of that, it is well placed for both overland and sea travel and with good connections both to Varric's network and the Freemarch Jennies. It would thus be much easier and quicker to respond to any threats that arise than buried down in the Frostback Mountains.