Head up or down when riding downhill?

I let them do whatever they want. The horse knows best how to handle iffy footing. How we want them to go in the arena, or ideally, is NOT always what's best or safest in non-ideal conditions.

I only check them if they get chargy to try to rush.

Up or down a hill is certainly not a time to expect a collected frame.

If I'm riding an intelligent, competent trail horse, I'd let them have their head. If I don't trust the horse's balance or intelligence, I'd keep their head at a medium height... not too high, not too low.

Horses have been walking down hills, for hundreds, if not thousands, of years.

I really don't think we should be telling them how to do it.

I believe you should let the horse have its head at all times unless you are doing something that requires contact (such as dressage/jumping etc). Otherwise there is no reason to.

I pretty much figure, the horse knows what the heck it's doing -- When going through some tricky terrain, I always let the horse have it's head to navigate, and all I control is speed and direction.

True, but they weren't really meant to do it with us on their backs!

My horse is still pretty green, especially to hills on trail...and she wants to see what the mud is so if I let her, she'd go down the hill with her nose IN the mud! I'm just concerned that if I let her do it, and she loses her footing or trips, that her head dragging the ground + me on her back going downhill would make her lose her balance and possibly end up with her flipping over.

Has anyone had any experiences like that?

The only thing I do is to control speed and direction. I've not had a horse that didn't know how to keep balanced with a rider while going down hill - why would I want to interfere with that?

I know what you mean. I will sort of help her up if she trips or starts to fall when going down hill. Vida doesn't watch the mud but she will try to grab a bite to eat on an uphill or downhill grass covered grade. Guess she figures her mouth is close to the ground, why not I'll check her up if she does that too. Otherwise she is on a loose rein.
Before Saro's lameness issue, I kept her on a short rein. She wasn't sure how to handle grades since she had never been on one before. Since she was just learning how to carry a rider and the balance needed I wanted to keep her and myself safe. Its more of a sometimes tight sometimes loose rein thing though, dependent on how she feels under you and how she is handling the grade. That said, I think the answer is more in the gray area instead of the black and white.

My mare's an experienced trail horse... I let her do what she wants most of the time... but if it's a really, really steep hill, I'll keep her head at a medium.

My gelding isn't as esperienced, and he keeps his head at a medium naturally.

I agree, where I live it is very steep with rocks, stumps, etc. I doubt your horse would flip over, when i take my horse down a hill I look straight forward, and lean back, and let him choose the correct place to step.