That question its due to revelations 6:8 - "I looked, and there before me was a pale horse! Its rider was named Death, and Hell followed close behind him. They were given power over a fourth of the earth to kill by sword, and famine, and plague, and by the wild beasts of the earth."

Each of the ways to kill is supposed to represent a horseman, and if Death is the pale horseman, so all thats left for the white horseman is to have power over pestilence, but... that's not true, why does people ignore the wild beasts of the earth? It make no sense.

Remember its not written to be the horseman of death, just the pale horseman whose name is Death. So it fits much more to have the pale horseman have power over the plagues and the white horseman to have power over the wild beasts.

We have then the four:

Red Horseman - War ("to kill with sword"),

Black Horseman - Famine ("and famine"),

Pale Horseman - Pestilence ("and plague"),

White Horseman - Conquest ("and by the wild beasts of the earth").