Congrats on the new horse, I've been involved with TB's for years.
Lets talk feet for a minute - TBs are notorious for flat feet, thin soles - BUT THIS CAN BE REMEDIED BY CORRECTIVE SHOEING.
You MUST have a knowledgeable Farrier who will promote BLOOD FLOW thorugh the hoof. NOTHING can improve if the farrier does not do his job correctly to allow the hoof to have bood flow.
The angles of the hoof has to be in accordance to the horses pasturns, shouldres and hips. The breaking point has to be correct, the frogs have to be open and the heels have to be permitted to grow.
If your Farrier says that your TB is just how he is and leaves it at that - FIND A NEW ONE!
My TB had horrible feet because the farrier we did have was not doing his job properly, not that he didn't know any better - it was because he only knew what he knew. My TB had long toes, no heels, thins soles and couldn't keep a shoe on him if his life depended on it...until I found my currect Farrier.
Now my TB has THICK soles, HEELS and a proper toe with correct angles and a fabulous breaking point. Plus, my TB keeps his shoes on which is a bonus.
Also - Full Cheek Snaffles should be used with the keepers. The Full Cheek was created to lay in the horses mouth at a certain angle, and this is only achieved with the keepers used. When you use the Full Cheek without the keepers, the bit rests in the horses mouth at an incorrect angle.
You have a beautiful horse, and congrats again - please get a thorough vet check done, and find a Farrier who will trim your horses feet to promote blood flow and proper growth.