I'm all for visitation with horses in training.
The only problem i've seen with visitors that don't know any better is if their angel horse "Johnny" goes out and has a bad day, and the trainer has to correct and ride through it, "Johnny's" mom throws a fit and can't understand why her little angel had it a little rough during the ride.
However, if you as a horse owner can understand that your horse will have bad days, and you can understand why things are done the way they are, well - there's no problem with you visiting on occasion