No one would fault you for thinking the worst if you discovered your horse standing in his field, unwilling and unable to walk even a step. But before you panic, take a closer look and consider the possibility of radial nerve paralysis rather than a broken leg.
Radial nerve paralysis occurs when a kick or other blunt blow traumatizes the long radial nerve, which runs down the front of a horse's shoulder. It can also develop after a horse is anesthetized in a position that compresses the nerve for a lengthy period of time. Damage to the radial nerve leaves the horse unable to advance the leg, and horses will often stand with the shoulder of the affected leg "dropped" with that hoof knuckled over to rest on the toe.
If you find your horse standing in the field with a dangling leg, first—obviously—check for open wounds or other signs of fracture. Also observe the horse's demeanor. Radial nerve paralysis isn't particularly painful; if the horse appears agitated or in pain, call the veterinarian immediately. If all looks well, very, very carefully attempt to place the hoof of the "limp" leg flat on the ground. If the horse allows you to do so, you may be dealing with a case of radial nerve paralysis. Call the veterinarian and let her know what you're seeing.
The prognosis for radial nerve paralysis depends on the extent of the nerve damage. Mild cases may resolve in a matter of days with anti-inflammatory medications and DMSO. Your veterinarian is likely to wrap the affected leg as well as the opposite limb to ward off laminitis. Severe cases of paralysis, however, in which the nerve has been completely severed, can take months to heal or may never improve at all.