Can a horse breakout of a lead in Minecraft?

I put a fence down and tied up my horse with a lead and went exploring. But when I came back there was no horse or lead or fence.

But then UNBELIEVABLY I was able to find the horse just wandering around(that saved me from walking home LOL)

Is fencing a horse in the only way to keep it form running off?
I'm sick of losing my horses and my saddles!

Sometimes a lead will break if your pulling an animals and it gets stuck and you move too far away. But no way no how it was able to break the fence or lead while it was there. Something else must have happened which broke the fence, thus breaking the lead letting the horse escape.