Originally, the expression “to hold one’s horses” had nothing but its literal meaning, to keep one’s team of horses from getting excited.
In the United States somewhat more than a hundred years ago, however, the expression began to be applied to people, always as a mild adjuration.
And because of an assumed rustic source, the suggestion that one control one’s temper or patience is generally phrased, placatingly, “Now, just hold your hosses.”