I think the color bar in rated hunters is pretty much a thing of the past.
What circuits and divisions are you looking to show in? I mean, the Regular Working divisions at the As are all still pretty much bay, chestnut and gray, but in the opens and the ammys you see all colors and coat patterns.
However, movement is a pretty big part of what hunters are judged on, and the horse either has hunter movement or he doesn't. Yes, movement can be improved, but if the horse doesn't have the length of stride, and daisy cutting movement, swinging freely from the shoulder, he's not going to do well as a hunter. I happen to love TB/QH crosses, and have known a couple to do well in the hunter ring, it's really down to an individual horse and their confo and training.
Also, depending on how competitive you want to be, if the horse can do the striding and does well over fences, maybe you don't care if he can't pin in the hack.
Get someone with some hunter ring experience to look at the horse or look at a video under saddle and advise you about suitablity for the hunter ring.