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I'd like to think the wedding scene played out on the other side of the gazebo, the side facing the wall, so no one saw what was happening and no one actually knows they tied the knot until Quizzie goes around whispering the news to their friends, and that's why the courtyard was empty. In the conversation just before the scene plays out they agree that getting married in the middle of the council would be awkward and Cullen says they know people who can keep a secret, so I think the wedding wasn't supposed to be a grand public ceremony, but just the two quickly eloping behind the gazebo on impulse.
Well, at least I prefer to think like that because I always imagined my IQ and Cullen randomly eloping one day and getting married in a tiny Chantry in a small village, maybe when they were visiting the noodle siblings or something, then coming back to Skyhold and going, so yeah we're married now, surprise. But a quiet, discreet corner of the Winter Palace works too. 
Of course, once Josephine got wind that the Inquisitor and her Commander are married and she didn't even get to plan a huge event for it, she would totally force the two to put on a huge party and get fake-married again in front of all royalty and nobility, etc.