Horses are often put down when their leg is broken for several reasons:
1. It is very expensive to fix a horse's broken leg
2. The process of fixing a broken leg is very stressful for a horse
3. The chances of it fully healing are slim.
4. A horses legs are so important to them; if one cannot be used, it will affect the entire body, often causing even more problems, like what happened to Barbaro when they tried to fix his leg.
It is simply less stressful and less painful for the horse to put him down, and cheaper for the owner.