This is how people process this. But, it is absolutely wrong as horses do not look at it this way.
Most of what you have posted I agree with, however I don't agree with not letting horses look at things or investigate things.. My horses are allowed to look, they must keep walking but they can look all they want. I want the to enjoy going for a ride, not do it because they have to.
They do not keep going forward because they have to. They go forward because:
1) they trust you as the leader.
2) with you as their trusted leader, they do not feel that they have to examine things.
They are not only perfectly happy letting you decide for them. They are A LOT happier because they do not have to worry about anything.
As far as TL goes:
I would do two things right away:
First, I would get a deep seated stock saddle with big swells on it for trail riding.
Let me explain where I am coming from. I am 65 and have horrible balance any more. My back is so bad I can no longer lope a horse and sure cannot work a cow any more. I have Rheumatoid Arthritis, Osteoarthritis, Degenerative joint (disk) disease and severe Scoliosis. My MRIs would pass for a 90 year old with a bad back. My Dr. says I should not be able to walk much less ride. I have two younger brothers that have had multiple spinal surgeries and are complete invalids. I am convinced that my insistence to keep riding as much and as long an I can is the only reason I am walking and for sure, still riding. My Dr. just shakes his head. On top of my back problems, my hips and knees are also about gone. My hips were both injected about a month ago. Again, Dr. just shook his head.
So, you cannot still ride with a greater handicap than I have. Somewhere in this degeneration of my body, my balance went out the window. I have taken a couple of pretty hard falls in the past year. So, I am riding a saddle with a deeper seat and looking for one I like better. I have always ridden a saddle designed for reining training, but they are not deep enough and I can't stay in one any more.
Secondly, are you making your horse suffer any consequences for spinning around? You should! If your horse ducks around to the right and you don't go off, You should instantly snatch her head to the left, kick her her in the right ribs and spin her 3 or 4 times to the left. I have found that when I do this with a green horse, they hesitate and start 'spooking in place'. You cannot stop a horse from being a horse. They are a prey animal and are 'hard-wired' to keep themselves safe. It is our job to constantly remind them that we are in charge, that they need to trust us completely and that we will not accept spooking and bolting.
These are the methods I have not only used to make good trail horses, but they are the methods I have used to train horses for CLEET certification for horses to be used as police horses to work in riots and big crowds. If you can train a TB or TB type horse for police work, a trail ride in the woods should be a piece of cake.
Like a good trail horse at my house, a police horse is never shown a 'booger'. They are just taught to trust their rider and follow directives given by that rider. They are never taught to examine things. That is the last thing you want them doing.
[If it makes you feel any better, your horse is a superb athlete. It takes a really athletic horse like a cutting horse to do a 180 so fast that it 'drops' in the front end. This is one of the things we look for in a good cutter or cowhorse.]