I know I've already said this..... BUT here goes again.
Seriously the first thing to do is get the horse's hooves looked at. Especially if your farrier is trimming them "like a TWH". Take a look at a show TWH hooves.... is that what you want a farrier doing to your horse? Just because it's a TWH?
Other people have a good point that it may be a balance issue that can be solved by training and riding, but you need to get his feet looked at.
Let me tell you the whole story of my mare.
My parents bought this mare along with her 1/2 sis when I was like a year old. They bought the 1/2 brother a year later. Flame was a serial tripper. This continued for years to the point where she had actually fallen on me 15 or so times throughout my childhood. I'm apparently a moron because I continued to ride her regularly, but in my defense the tripping happened probably 5% of our rides together. Anyways, she damaged her knees from falling so often so developed arthritis in her knees and so was retired from regular riding. I went away to college and my parents took care of the horses. They went through the typical succession of farriers never finding one who was reliable (the most important quality to them) or who did a good job (important to me). Somewhere along the line they found a guy who was reliable!! Yay!! He also *GASP* knew how to trim a TWH's hooves!!! Oh how wonderful, my parents thought. I came home for a visit and just about puked looking at the horses feet. They looked like they belonged on a cow. LONG toes, no heel. Around this time I noticed that Flame no longer did anything but walk in the pasture and she was tripping constantly now. I had no money (or clout) to get a proper trim on the horses so it had to stay the way it was.
Skip to the end.
I moved home and became interested in trimming. My friend had been learning from 2 different farriers as well as going to several Ramey clinics. She agreed to come out and trim my horses. Long story short after 2-3 proper trims Flame started gaiting/trotting/cantering in the pasture again. I even got brave and took her out on some rides. No tripping. NONE. She was about 27-28 when this occured and was good for about a year. Then she hurt herself and can't be ridden againg, but that's a different story.
I'm sorry but I get really leary when I hear "knows how to trim TWH." I'm sure that other trimmers had something to do with her issues as well as us causing problems with riding/balance, but that last trimmer really caused her a lot of pain. JMO. *steps off soapbox*