How did the Cavalry Feed Their Horses on The March?

After riding "40 miles a day on beans & hay", the federal cavalry during the American Civil War had to allow their horses to graze and eat enough to replace the calories they burned while riding hard on campaign. How did they do this without the horses running off, or having to hold the reins the whole time? This week on the 11th OVC, lets learn how the cavalry allowed their horses to graze...