I think the biggest cause for worry would be loose straps. Snug the belly straps so there is no space, no loose straps that they can get a foot caught in. Otherwise, if they catch it on something, it might tear, they may even rip the straps, but I've never had one get injured. Heck, Cyn caught the neck of hers on the gate hinge when she climbed out of her stall and it tore through and was left in a pile within three steps.
Horses can hurt themselves lots of ways, of course, but in my experience, they are stronger than their blanket.
LOL, both of us thought of Cyn's fiasco. That was a pretty extreme case wasn't it.