I was following Barbas to Haemar's Shame when I see three figures approaching from the opposite direction. The weather was foggy so I don't recognize them immediately. Usually it's either a patrol of rebels or imperial that walk in group of three, right?

Not this time. I hear a female elven voice screaming "Die, foul beast" and, at the same time, a shower of lightning bolts pours over the poor beast. Not impressed, Barbas charges and a battle quickly ensues. Amused, I approach the three elves surrounding Barbas but they seem to completely ignore me. I gently hit them with the blade of my sword to see if there's some reaction but, no... they're too busy battling the seemingly immortal dog to notice me.

Ok, I step back a little and watch the battle. The Thalmor justicars are no easy foes but one after another they fall to the ground dead: Barbas is an aspect of a daedric prince, after all...

Thalmors attacking the player is a random event; I was amused to find that, they seem to hate more dogs than the dragonborn! The battle cry "die, foul beast" was obviously not directed at me (although Thalmora have a very low opinion of everything that is not Aldmerish).

Barbas is annoying but will turn any fight into an entertaining show. One of these days, I will check if a Giant can send Barbas flying or at least make him stop barking!

The Thalmor despise the daedra. The dunmer were kicked out of Summerset/left of their own accord because they wanted to worship the daedra.

Wait, seriously? Do you still know your source? I'd like to play a Thalmor character, but there's not so much fun to it anymore if I can't help the daedras a bit. He needs to be evil, and the daedra quests are the most important ones on that part (and kind of the only ones).

TES is the source. Play the previous games....

[....and of course, Barbas isn't a "dog" per se - that's simply his outward appearance in Tamriel....]

Not even just the Thalmor despise Daedra, High Elves on the whole hate them. The origins of the Dunmer race have them as Chimer, who are physically indistinguishable from High Elves. The Chimer were basically Altmer who wanted to worship Daedra and left the Summerset Isles/were forced out, and began a pilgrimage to Morrowind. At the time Morrowind was populated by Dwemer/dwarves, so the Chimer went to war with them. As punishment for the death of the Idoril Nerevar, Azura cursed the Chimer and turned their skin to ash and made their eyes blood red, and that's how the Dunmer as they're known came to be. It's covered beyond extensively in TES III: Morrowind, since in that game you play the Nerevarine, aka the reincarnation of Nerevar.

Probably in one of Vivec's books, too, I'll have to paw around the internet for those...

Indeed, I know the lore; I found funny that they recognized him on the spot. Maybe it's just a product of a random hostile encounter and the dog is just treated like any other companion, but it would be really a nice touch if Barbas is indeed treated like a Daedra. I haven't found any vigilant of Stendarr on the roads while I was travelling with it, but I do wonder if they also recognize him:
"DIE, daedra worshipper!" "Wait, it's just a cute little puppy!"

Oh the Thalmor on the whole seem to dislike dogs, maybe even all High Elves. The guys that follow Ondolemar in Understone Keep always make remarks like "Stupid dog" or some sort of rib at the dogs. Even when you restore the Gildergreen and that pilgrim stands outside Whiterun stables with her dog, she is always all "Damned mutt."

And when http://www.uesp.net/wiki/Skyrim:Ondolemar abandons Understone keep after Diplomatic Immunity, he leaves behind his two soldiers and the two dogs.

I thought that these two dogs belonged to the jarl of Markath?