Still, I do not think that stampeded horses are quite so crazy as cattle, and they get over their fright quicker.
Let me try to illustrate a little better an actual stampede.

The night was calm, clear, but very dark--no moon, and the stars dimmed by fleecy cloud strata.

The herd of some 2000 steers was bedded down, and had so far given no trouble.

Supper was over and the first guard on duty, the rest of the men lying on their beds chatting and smoking.

Each man while not on duty has his saddled horse staked close by.