Curse whoever put that stupid hat on him.
I can't tell you the number of times I've looked at that scene and gone, "Whose idea was that? And why did nobody think to tell them how horrible it was?"
I'm less annoyed at the hat itself and more how it passes into his fricking face! Doesn't that hurt, Solas? D:
I also can't tell you the number of times I've watched that scene and gone, "That looks painful, Solas. Like, really painful. Are you okay? Because it looks like that hat it about to amputate your nose."
He's wearing the "Helm of the Drasca" (which can also be found in the game) and it's description says "Rumors persisted that the Drasca continued on and played a part in the Anders rebellion against Orlesian rule following the Second Blight, but if that is true, they subsequently drifted into obscurity once again." '
You know... this doesn't make me feel any better. 
Someone made a dialogue wheel for the balcony scene with options for addressing the hat:
- "Is that Inquisition regulation?"
- "You look hat-tastic tonight."
- "Um............ hat?"
- "The F*** is on your head?"
I think there were a few more... I'll have to find that image...