We have at least one TWH and a couple of pacing STB horses working as staff horses in our hunt. All get where they need to be just fine, including galloping and jumping. All go in the field just fine, too, including first field. Top end speed may be an issue depending on the hunt, but in trappy country a sure-footed horse gets there just as fast as a TB who can’t go full out without crashing.
I’ve trained a couple of TWH as hunt horses and it was dead easy because they were already solid trail horses who had good brains. The only drawbacks I can think of 1. a weakly gaited horse is more likely to break gait when ridden with w/t/c horses (not a problem in your case, and just a matter of training to compensate–including the option of just making it a w/t/c horse) and 2. jumping out of a gait like a running walk or pace doesn’t give much impulsion. It’s nbd for small stuff, but (IME) a lot safer and easier to jump from the canter as the jumps get bigger.
The only other drawback is that some gaited horse trainers swear that gaited horses can’t/shouldn’t be rate-able speedwise. In other words, the only way to ride gaited is to get on and go as fast as possible and refuse to ride with horses who don’t go exactly that speed. IME, that’s stupid. It’s a horse: of course it can go different speeds. I’ve ridden over a dozen different MFT, TWH, and pacing STBs. Every single one of them was quite capable of learning basic dressage self-carriage, jumping, riding in a non-shanked bit, adjusting speed to match the group, and gaiting while the rider is correctly balanced in the saddle (not sitting on the loins). So, depending on the horse’s history, you may have to put some proper training into it.
Go! Enjoy! I’m a dedicated TB person, but all the gaited horses I’ve known have been darlings with great brains.
