Scout Harding was just the cutest and I wish that was a thing. I love dwarves man. Harding is just second in a list of dwarves I wanted to be romanceable. (Varric x.x)
Umm... Harding is romanceable. You have to flirt with her at the first location where you meet her the first time, and then it'll unlock the flirt option at the other locations too. When she's back at Skyhold you can then initiate a romance with her when she asks whether you're serious, or just messing around. If you continue with it she tell you her first name, Lace. However, if you start a romance with any other companion then she slips back to strictly professional without a break up scene.
I had a Qunari Warrior with Harding as his love interest at the end of the game. That must've been quite a match-up in the bedroom, especially with her fear of heights. XD
If you don't romance her, Harding comments that both Dorian and Josephine have been 'friendly' with her, as long as you're not in a romance with either of them. Josephine even goes as far as sending the scout flowers.