Just because someone is scared, doesn't mean they don't love horses or want to get braver. I have always been a scaredy cat and horses actually help me work through my fear issues.
Once I am comfortable on a horse, I can trail ride them by myself and do just about anything with them, but getting to that point can sometimes be hard.
For instance, I now have a 3 yr old gelding and every time he bucks or seriously spooks I feel like the sky is falling. I stay on and ride and correct the issue, but it shakes me up so badly I often go home and cry about it. (Falling off can set me back weeks). But that doesn't mean I don't want to get to a point I am comfortable on the horse and I am still working on that. I know I can get there if both the horse and I get a little more confident and get more mileage under out belts. It's not that a person doesn't have the passion......I have been addicted to horses since I was in kindergarten. I don't think anyone can love horses more strongly than I do. It's more of an anxiety attack or something along those lines. Kind of like you just missed a car accident and your brain is telling you, "wow, I could have gotten hurt just then."
Yes, make sure it's the girl's idea. No use pushing her if she doesn't love horses. But if she does love horses, then working through her fears with horses can help her work through her other fears in life. Because I doubt her fear doesn't show up in other areas as well. It's no fun being scared of everything.