When you are on a very natural horse, that low head set is natural...
Think of it this way, when you're riding a dressage horse, who has lots of collection and impulsion, when you give them rein where does their head go? Generally down (such as the free rein walk), many many dressage horse will also work at a trot and canter at lower head level if you allow them to have that rein.
Headset isn't made on a real natural horse, when I get my pleasure horses (even my reiners) engaged, using themselves, and lifting their shoulders their headset falls where it naturally wants to fall.
On my pleasure horses they have a lower neck set, at least thats what most breed for, and thus a lower headset comes naturally when you work them.
Look at our guy. This was in February, he was 23 months old, had less than a month of handling other than a bit as a weanling. He has no muscle and he still has a lower headset. I should get an updated video, but he carries his head even lower than that now...
We have done absolutely NO work asking him to put his head down in anyway, this is how he likes to carry himself. And as he gains more strength he holds it lower.
So to sum my point up, the head falls where it natural falls when you get a horse using themselves properly. Some WP horses are level, some of just below level and some are a touch above it.
I like my pleasure horses level or just below it. I don't like the ones that drag their nose in the dirt either. But those ones tend to be WAY on the forehand too.
These horses have tons of life, just becacuse their head is down doesn't mean a lot has been done to break their spirit. It's just natural for them based on how they are built.