I know several horses that do dressage barefoot and they are absolutely fine. Besides, shoes limit the natural movement and circulation of the hoof, sometimes even numbing them, thus some people like them, because then the hooves are less likely to become ouchy. Hence the idea that shoes "protect feet". Barefoot definitely calls for more attention and care, but it is worth it.
That said, I respect people who have chosen to shoe their horses and do not intend to start a barefoot vs shoed war here. :)
I completely agree that barefoot is best if your horse has good feet - I used to compete my last horse in endurance barefoot, and he never batted an eyelid. Dressage would never have been a problem for him. My current one, however, is practically lame without shoes, and has very crumbly feet. I end up shoeing him every 5 weeks just to keep him happy in the field! But he does everything fine with shoes on.
However, I'd love to know where you heard that shoeing numbs feet. Shoes can cause lameness and balance problems if not done properly and in balance with the foot, but if done properly neither the shoe nor nails should go anywhere near any structures that are innervated or even have blood supply - therefore should have no direct influence on either pain or numbness, only indirect influence on muscle, tendon and joint pain if the balance isn't correct.
It's an interesting theory as to why some horses are 'footy' without shoes, but I struggle to see how it would work with the anatomy of the foot and the biophysics behind correct shoeing. I'm not trying to start an argument, but it goes against everything I've been taught as a vet student, and have seen through work experience alongside (admittedly excellent, award-winning and vet-respected corrective shoeing farriers). I'd love to hear the full theory behind it, just out of curiosity.
Again, if the horse goes fine without shoes, then go for it - it's more natural, much less expensive and the hoof does get stronger the longer it is unshod. However, I'd advise against shoeing for the competition season and then taking shoes off over winter - taking shoes on and off will reduce the quality of the hoof. I;d advise picking which route suits your horse best, and sticking to it (: