We have a good sized mounted shooting club based out of my barn. By far the stock horse breeds are most popular, but every now and again you come across something different, including draft crosses. I can't say I've seen a TWH or SB, but I know it really takes time to get to the point where you need a horse that can be QUICK. If your horse is obedient, then starting (especially for your husband, who you said is a new rider) on the horses you already have would be fine. Who knows, your horse might be better at it than you think! Besides, that smooth movement might make it easier to hit your targets, you won't be bouncing around!