This is a very interesting subject that school owners discuss regularly. We all have stories of folks that came to our school with very little horse experience (for whatever personal motivations) and became very successful as professional farriers because they had excellent people and business skills.
Then there are lots of stories about people with very good horse skills but lack personal drive, common business sense and/or poor people skills and they didn't last six months as a farrier.
The conundrum is trying to list admission requirements for students entering horseshoeing schools so that the vast majority of the graduates are long-term successful farriers. For every recommended requirement you can list, schools have lots of exceptions that would render that requirement unacceptable.
Success as a professional farrier is in the intangibles. It is what is inside the student. Shoeing horses is hard physical work and so, to be successful, shoeing must 'charge your life batteries' or you will eventually be moving on to another profession.
I rarely have a student that has not made significant discoveries about themselves while they attended school, regardless of whether they shoe full-time or not. Shoeing schools can be a good life experience even if it is not a career decision.
A student with no horse handling skills may to have a tough time gaining the maximum amount of education from any school. It would be very important that the everyday instructors have many successful years shoeing and posses horsemanship skills related to ground handling horses.
Once a student has narrowed his/her search to a few schools it would be important that they call and speak with the person that will be training them; not the owner or a secretary but their actual instructor. Ask questions about the teachers teaching style, their philosophy and expectations of students. With just a short conversation most students should be able to tell if they are compatible with the instructors teaching style.