Wandering Woodsman

One of the unique things Dragon Age: Inquisition did was to give every companion hanging out in Haven in his linen garbs character their unique set of display style for armor items. So the same armor item will look different on Solas than it would on another character, and it gives a bit of personality to your characters. Solas's style in all of his armors follows a trend. Each armor type has roughly three specific variations, and for Solas, they go from shabby robes, to lots of cloth wraps, to finally a fancy fur wrap. All versions of his armors and robes go over the default linen garbs he wears outside of combat. Despite all the variations, one thing remains constant: his camping kit.

If you take a closer look on all of his outfits, he will have a small travel pack with some tools and a very visible cup hanging off the pack. Based on what we know of Solas, this fits really well, as he is a wandering hedge mage who does not have a fixed home, so having a neat travel pack makes sense. It's also rather cute that he seems to be always ready and prepared for journeys. His outfit is something that's so particular, your other companions even make a note of it (and give him a bit of hard time over).

Solas, what's this whole look of yours about?
I'm sorry?
No, that outfit is sorry. What are you supposed to be, some kind of woodsman? Is it a Dalish thing? Don't you dislike the Dalish? Or is it some kind of statement?
Well, it says "apostate hobo" to me.
(if Vivienne is in the party)
Unwashed apostate hobo, more specifically.
Dialogue with Dorian (about Solas's clothing choice)

Like other mage class characters, he carries his staff on his back when not in combat, but since he always wears his cute camping kit, the backpack has the added advantage of providing a nice spot for his staff to hook in to. In other characters, staves do the usual mystical stick on or float on their back, but Solas's backpack design makes the staff placement look natural.

showing off his travel pack while getting some action on

As is custom for elves, he goes barefoot (elves who do not grow up in cities typically do not wear silly human shoes). So perhaps this was one tradition the Dalish got right, since Solas follows the old ways, and he gets his knowledge from his travels in the Fade. Though unlike other elves, Solas does not bear any facial tattoos. Dalish elves typically honor their respected gods by marking their face with that specific god's markings, and city elves have varied on tattooing themselves throughout Thedas.

His shiny bald head though, which can be seen better in this picture, is never specifically explained, though it's possible he lost his hair with age or due to his brand of magic. When Inqisition promos first came out, and I got a look at Solas, I have to admit I was initially disappointed he was so bald, but after a while the baldness grew on me and now I think his design is rather perfect. The bald head adds character, and Solas himself certainly seems to take it in stride.

In the post-ending DLC story, Trespasser, Solas's outfit has a noticeable change; he wears actual metal armor, and his fancy fur wrap gets a significant boost. Once his full story has been revealed, his outfit change makes a lot of sense, as does the implication of his outfits through the game.