I do not think Solas/Dread Wolf is bound to Mythal in the same manner as the person who drank from the well, or bound in any manner what so ever. This is mostly based off of the developer notes that were found detailing the epilogue scene. Now of course I do not know if the notes are canon and the story can always change over time, but for the sake of argument, assuming they are canon, I can not see how Solas could be bound to Mythal based on the notes. Two lines in particular I want to focus on.
First is where it says "She knew that Solas would summon her, and that he would need to steal her power to further his plans."
Based on how this is worded, it would be weird to describe Solas as "summoning" her if he was bound to her. We would actually expect it to be the other way around, where whomever was bounded would be getting summoned by the person they are bounded to. In other words, the way its worded would actually support the theory that Mythal is bound to him more than Solas bound to her, though I don't think that is the case either. So I am quite curious what they were going for using the word "summon." Npt only that but note it says "his" plans, not their or her. So it also seems like his plan is not necessarily the same as whatever Mythal was trying to do all these years.
Second is "He was once her oldest friend, but she knows that in his drive to restore the elven people he will kill anyone -- even her"
This would seem odd if he was bound to her, as it shouldn't really be possible then for him to kill her. Though how its worded makes it seem if she didn't willingly give him her power, he would attempt to kill her, and might even possibly succeed. Which would kind of also show how crazy Solas has gotten since he stated he created the veil because Mythal was murdered, now he would murder Mythal himself to undo the veil he created due to someone else murdering Mythal.
Also I want to note what is said in the beginning of the epilogue scene. Mythal says "You shouldn't have given your orb to Corypheus." That would seem odd if he did it because he was bound to Mythal and it was the will of Mythal. She speaks as if what he did would not have been what she would have done/wanted.
And one final thing, the developer notes mention that she would give her power to solas "so long as she can pass the essence of her godhood onto morrigan." So it also seems like Mythal didn't actually "join" with Solas, Solas just took her power, it more seems she joined with Morrigan, of course Morrigan willing. Now what does "essence of her godhood" mean? And how is it different from her "power?" Don''t know.
Personally I think Solas is the baddie, though Mythal may be no better with her "vengeance". I also think there is some credence to the idea Solas may actually be a spirit similar to Cole, and maybe even all the Evanuris are like that. Solas specifically being a spirit of wisdom/demon of pride. In the end it just seems like his pride is pretty much the cause of, well, the end of the world, possibly the end of the world twice, if he succeeds. Since as noted, he would even kill Mythal, that to me sounds like he has a singular focus that he can never stop and it trumps all else, kind of like cole, kind of like a spirit, and kind of like Mythal with her vengeance.