The answer: It depends.
Until very recently, a broken leg was almost always a death sentence for an equine. Horses cannot stay down for extended periods of time - they will literally die of organ failure. A horse that can't stand can't live. In modern times we can sometimes support a horse in a special sling - this is often done for horses with serious leg injuries or when trying to save an animal that's become too weak to stand because of illness or malnutrition.
It's also possible, these days, to pin a horse's broken leg back together. If you're working in a lower tech level, though, it's likely to be the norm for a horse with even a simple break to be euthanized. Even with modern technology, only horses of considerable value - and suitable for breeding - are usually saved. It's likely the horse will be permanently lame even if it survives. However, some horses with simple breaks or fractures can make a full recovery with modern veterinary technology.