Lavone (human mage) fell off a horse as a kid and thus is terrified of horses. It wasn't until she found the war goat hart that she finally started riding again. It's sleek form, it's deep eyes and it's terrifying scream as it swooped down on her enemies was enough to make her fall in love. She spent a lot of time with it, riding, washing, brushing and feeding it.
Adair (human warrior) had a horse, which he was quite fond of. He didn't use it much when on missions, but sometimes he'd take it out of the stables and go for a ride by himself. He might occasionally feed it some sugar cubes.
Cressida Cadash sometimes donned her cowboy hat and rode around on horses when she tired of riding the Bull. She wasn't particularly connected to her horse, but she preferred it over the other mounts. Harts smell, Nuggalopes where too wide and Drakolisks where icky. How did she get on the horse? Upper arm strength, 30 pull ups, very morning, using Bulls arms as the bar.
Bergstein Cadash was terrified of heights. And if his companions had tried to lift him on a horse, he would have literally stabbed them in the face. (And that's the correct use of the word mind you). He also disliked being around things with large legs (unless he was killing them) so he felt distaste towards all the mounts. And then there was the whole issue of: don't play with your food.
Vedis Lavellan fancied riding out on a white stead, but she could never say no when her nuggalope made (whatever sound it made) so if she went riding, she usually rode the nuggalope. It was cuddly and it had hands.
Isalath Lavellan was her own mount. No horse/hart/nug/drakolisk for her.
Mytjan Lavellan rode around on the Iron Bulls shoulders. Occasionally Bull would pick him up and fling him at the enemies. Mayhem. Mayhem everywhere. (But I think he had a Hart he sometimes used, reminder of home and what not).
Kaliesa Aadar was worried she would crack the mounts back, so she didn't ride if she could walk. If she had to ride it would probably be a horse.
Shira Aadar reveled in the fear she got as a Qunari Necromancer, so she preferred riding the dracolisk or the bog unicorn.