LOL, I had no idea Cully's fuzzthing was so disliked. I've always assumed part of the reason it was added was so there would be soft furry cushioning for hugs. Even if it is decorated with battle dirt and sweat, as some here have theorized. His armor in DAI also looks much slimmer than what he had in DAO and DA2. He'd probably be bumpy to cuddle otherwise and it seems like it could be awkward. I wonder what it would be like to have a heavy armor wearing Quizzy hug a fuzzless Cullen during the prayer scene...I imagine it would sound a lot like clanking tin cans. Cute and heartfelt clanking, but clanking nonetheless.
But he does look incredibly dashing without the fuzz. sigh 
Huh... do some people headcanon that they try to keep the relationship a secret? I've always imagined Cullen being very open about it - not the details, mind you, but when he and the IQ decide to spend some time together (in my headcanon they have dinner in her quarters every night after the romance starts - no sleeping over, though
) they're very upfront about it. No more sneaking around and making excuses, like he may possibly have had to do with another Circle mage back in the day... 
I felt the same way. Cullen seems the type to be very honest about things, and I feel like he'd have no desire to hide his relationship with the Quizzy because it might imply he was ashamed that he was doing something wrong. He is worried about what the Quizzy thinks of their relationship, but he's absolutely being genuine on his end and I don't think he personally thinks any aspect of the relationship is problematic. There's no power imbalance because he gets an equal say in things and you're both two consenting adults, so it's nothing like the situation between him and the Warden back then (And Inquisition reveals that canonically nothing happened between them because he didn't want to be inappropriate, though of course we're free to headcanon that something did happen if we want).
Also, I like to headcanon that he's secretly very proud that he's in a relationship with such a courageous and capable person. She's so cool, the world ought to know, I'll taunt Mia by "accidentally" letting the fact that I'm dating the Quizzy slip and then annoy her by not saying anything else because that's the brotherly thing to do, I have an amazing warrior girlfriend and I don't want to brag (but I do) - that sort of thing. He does say it would be a pity if there was nothing for the people to gossip about even though he'd rather some of the details be kept private, after all. 