My Fox Trotter Isabelle is a little like this. I have never had her fall off the trail or anything, but it's like she is insecure and sight-seeing the whole time we are going out, and if there is a bush or limb or anything like that in front of us, she will go right through it or trip over it like she isn't even aware it is there.
That is a little bit different than what I am used to, because my Mustang is so self-preserving.
It's not that Isabelle is blind or dumb, but it's almost like she is looking so hard for buggers in the bushes (or in her case, birds in the bushes) that she really doesn't look where she is going.
What I have found helps is to ride her more assertively. To give her a little more leg and more steering, whereas with my Mustang I can just sort of point and go. But if I am more assertive with Izzy, she wanders and sight-sees less and goes out better. So in a way I feel she is making me a better rider, because she makes me think, and my Mustang is so perfect that I get lazy.
Going back she is like a homing pigeon, so I don't have to ride assertively going back.