Shin splints are stress fractures. Some horses get overworked, and thus it occurs in their front legs. Hard impacts, over exertian, or rough/uneven terrain are some things that can cause it, just like in humans.
Basically, just stop training...There's not much that can be done and they take a long time to heal. I'd get a vet for some painkillers but that's about all that can be done.
I don't think horses have shins :P. You mean their cannon bone, but never mind that, like the above person stated they're just stress fractures. Just like in humans the horse need some time off, and then the horse should be good. It might also be wise to cut back on how hard her horse is working as that is why they form, because of overworking.