Yes, they are wild - they've become increasingly "tolerant" of people though as the 4x4 beach increase in popularity.
If you mean abuse as far as being hit by speeding vehicles occasionally driven by drunk drivers on the 4x4 beach, being shot at with guns and paint ball guns, being terrorized by kids on ATV's and being coaxed with food up stairs of beach houses where they're usually injured by falling through the wooden steps, then yes. Cans stuck on their hooves from people leaving garbage around, yup, that too, as well as numerous other assaults.
It's upsetting to those that live there and have lived there because the beaches that were once the home and safe haven of the wild horses, that they shared with a few small, scattered fishing villages are now jam packed with tourists, vehicles (see above), homes, etc..
By law, you're not allowed to be knowingly within 50 feet of a wild horse, however, you can always witness people walking up to them, feeding them and sometimes chasing them. Countless horses and foals have died from eating what tourists give them.
I don't think it would be as much of an issue if people respected the horses, the locals and the laws. The 4x4 beach is open to anyone that has a 4 wheel drive vehicle. I was nearly hit, along with my then 13 year old, when a Jeep Cherokee decided to go speeding down the beach, hit a ditch and lost control of his vehicle.
They are wild, but very used to people. We were just on Corolla about a month ago and you potentially can get close enough and touch them. However, you are required to remain 50 feet away. Does it always happen? No. Are people complete idiots? YES
If a horse steps on your towel, you are to back away and wait. No one does that though. Its very sad. They are terribly cute so I can see why, to non-horse people, its so tempting to get close and pet the cute poneighs.
Horses in the past few years have been shot, hit by cars, chased, etc.
When we were there, there was a foal that died because people were feeding the mother, and the foal ate it too, and colicked and died.
The Corolla Wild Horse Fund does intervene when they need to (animals in severe distress) because they want to keep the numbers up - I think they are a bit down this year.
Its very sad, seeing these bands, knowing that eventually they will no longer be there, because of tourists (hey, myself included) encroaching on their territory. The only good part is, where they live, there are no roads. Its a 10 mile stretch of beach and you have to drive on the beach to get to your house. So its not very populated.