After much thought and debate, Solas probably doesn't have a daemon. I say this because we don't know precisely what he is - if he's like Mythal and borrowing bodies, if he's actually a straight up spirit, or
something else entirely. I, personally, subscribe to the idea that he was just an exceptionally powerful elvhen mage - and I don't think he's in a similar state to Mythal. I don't subscribe to the notion that
Solas = Felassan, but that's neither here nor there.
So, not knowing Solas' true nature, but knowing that he spent oodles of time in uthenera, swanning around, I'm going to say he'd have no daemon (unless the daemon is a spirit, the snowflake).
That being the case, upon realizing he's in a world where people have daemons, he'd have trained a dove to be his.
Doves are innocuous (if fucking obnoxious shitheads) creatures, generally symbols of peace, etc.
Totally has a wolf for a daemon.
Why you ask? Because wolves are tricksters and generally feared among the Dalish. It's only natural her soul, being so fucking twisted, would assume the shape of that which the Dalish despise.
Because it just occurred to me that the elven gods can assume the form of a dragon, as can their high priests (see a codex entry about how some dude took a dragon's form and was handed to Mythal for judgment).
It's possible that Solas would have a daemon in the form of a high dragon, and like the witches in the Golden Compass, he'd be able to travel long distances from it.
He'd still acquire a dove as a stand-in, though.