You need to register him in the official game owned Quarter Paint Club to halter show him. None of the Clubs he's in are that. 

I see, I also have this TB who is registered but cant show him?
https://horsefable.com/horse/1848411?t=history&i=1 

Never mind that is my bad, I accidentally clicked on the halter show box 

Go to his edit page and check his working paths 

All good then! Glad you figured it out :) 

I do wonder why my good Tbs are not earning well in halter shows even if they have pretty good confo 🧐

Do you have them tacked? tack provides a small boost to their show score even in halter. What are their skills like? Skills count towards halter shows. halter showing increases skills slightly, and you can also increase skills by sending them to careers. have you worked out what the ideal Breed Standards are for TBs and compared your horses to them? a 5 star horse that's 11 points off perfect BS will do worse than a 5 star horse only 4 points off perfect BS. All dark green doesn't necessarily mean a horse is closer to perfect BS than one with 5 dark green and one light green, you need to look at the actual numbers