I don't know how common it is for one to bite an arm off, but they can be real mean and will definitely bite you. I'll never own another Shetland.
Most horses are dangerous not because they are vicious, but because they are bigger and stronger than we are, and don't have much understanding of how fragile we are. A well-trained horse should, from an early age, demonstrate respect for the personal space of a human and obey him carefully. This means things like watching that he doesn't step on your feet or butt you with his head, moving quietly when near you, and so forth. Behavior like that tends to minimize injuries to the humans.
Some stallions are spoiled so that they become dangerous, because their handlers believe that "he's a stallion, he has to act that way, he can't help it." So they never discipline a large powerful horse and he gets more and more obnoxious, even dangerous.
Some stallions (and a few mares) are simply vicious. They have something wrong with their brains, and should be put down so that their defects don't enter the gene pool. Unfortunately some such horses are kept and bred because they perform so well at racing.
All stallions have the potential to be dangerous. One should never trust even the most angelic stallion (and I've had some really sweet stallions who never hurt a fly and acted like perfect gentlemen even when being bred). Some people are going to argue this with me, but I believe kids should never be near stallions because you can never tell. Stallions have been known to turn on a lifelong owner and savage him or her, even when handled by very experienced horsemen.
Many stallions bite, it is partly their nature and mostly boredom from living a mostly solitary life. Many stallions are used for riding and show, but some live alone and mostly unhandled until the two minutes he gets to "do his thing" once in a while. It isn't natural for a stallion to live in a small space alone, and without a lot of exercise they can become pretty impossible to be around. That said... a bite is common.... biting anything OFF is so rare I'll bet you'll never see another story like this.
Horses are a lot like dogs --- a lot depends on how they were socialized but a stallion is never a completely safe animal because of how they're kept pent up and isolated except at breeding time. They'll kill each other --- but a stallion kept with other horses is more mellow.