In response to this post.
I’ll focus on the initial reaction, within the first moments of the encounter. Depending on who you have in your party at the time:
Cassandra: Shocked and speechless, quickly shifting into defensive suspicion. She would hesitate to trust him, even if he says that he means them no harm. He is clearly a liar and a very powerful one at that. Cassandra would flat-out deny that he is a god and would feel a small amount of comfort when he agrees with her.
Iron Bull: “Well, shit. That is really not what I was expecting.” He’d have a hard time wrapping his head around what exactly Solas is and would be rather floored that he didn’t notice anything especially weird about him when they were working together.
Blackwall: I want to be snarky and say that he’d feel somewhat relieved that he’s now been one-upped in the “lying about who I am” department, but in reality I think his reaction would be to keep his guard up. It doesn’t matter if it’s a friendly face - Solas is clearly something big and powerful and they don’t know what his intentions might be.
Dorian: Shocked and fascinated. It would be something completely unlike anything he’s ever seen before. He knows of shapeshifting magic, but it’s rather rare - and he’s never heard of anyone being able to turn into the form of an animal that is not a direct copy of that beast as it is in nature. The six eyes and huge form is a bit of a giveaway that he’s not mimicking a normal wolf. While noticing that doesn’t necessarily lessen his shock, he is undeniably interested in the more academic implications of understanding precisely what he’s just witnessed. He would think the idea of Solas being a god is utterly ridiculous. The thought would never cross his mind. He would assume that the Dread Wolf is simply a manifestation of a form of magic that he never has never encountered before.
Sera: Nope. Nooooope. She doesn’t get it, doesn’t want to, doesn’t care. Don’t explain it to her. She wants out. Whatever the hell that was and whatever the hell he is, it’s just elfy mage shit. It doesn’t make him a god.
Vivienne: Flabbergasted. There are very few things that would leave Vivienne speechless. This would be one of them.
Varric: Strangely, I think Varric would be rather calm about it. Shocked, of course. Confused, certainly. But just add this to a long list of very, very weird shit that has happened in his life.
Cole: YAY MY FRIEND IS BACK!
The Inquisitor’s reaction is hard to say as a generality - as all OCs are different. For Isii, it would be rather complicated. She would feel like simultaneously bursting into tears and punching him in the face, though knowing how she is after the events of the game, there is a strong likelihood that she would try her best to harden herself and keep her feelings on the issue private - at least until she could speak to him alone. Her feelings about it are made particularly messy because she sees the Dread Wolf in her dreams repeatedly after Solas leaves. The realization that he had been there the whole time, that he had seen the nightmares and the replayed memories and all of those moments where she had thought about him, worried about him, wondered whether or not he was even alive… the fact that he witnessed that and still did not reveal himself to her would leave her rather upset.