It's really hard to compare a hard-keeper TB to your easy-keeper quarter horses. My trainer has a bunch of quarter horses who are on local hay and no grain and they are all fat, even though local hay has very little nutritional value.
I would suggest you give your horse as much high-quality, orchard grass hay as he will eat, even when he's on pasture keep a hay net in his shelter. I also have a very hot TB. I really like Purina Equine Senior Active Healthy Edge. It is high in fat and low in starch, I was able to drastically reduce my horse's grain when I switched him to this as it was actually making him too fat! It doesn't make him hot (at least not hotter than he is naturally) and it keeps the weight on. I also add Canola Oil to his grain for extra fat (canola oil is better for your horse than corn oil or soybean oil because it has a better omega-6 to omega-3 ratio, although even better would be Cocosoya oil, which is made for horses). I've also heard good things about Cool Calories 100 (a weight gain supplement) and rice bran. Hope this helps :)