Excerpts from Revelation 6:1-8, New International Version
"I watched as the Lamb opened the first of the seven seals. Then I heard one of the four living creatures say in a voice like thunder, "Come!" I looked, and there before me was a white horse! Its rider held a bow, and he was given a crown, and he rode our as a conqueror bent on conquest...
"Then another horse came out, a fiery red one. Its rider was given power to take peace from the earth and to make men slay each other. To him was given a large sword...
"I looked, and there before me was a black horse! Its rider was holding a pair of scales in his hand. Then I heard what sounded like a voice among the four living creatures, saying, 'a quart of wheat for a day's wages, and three quarts of barley for a day's wages, and do not damage the oil and the wine!'...
"I looked, and there before me was a pale horse! Its rider was named Death, and Hades followed close behind him. The were given power over a fourth of the earth to kill by the sword, famine and plague, and by the wild beasts of the earth."
I'd suggest that the ways in which they destroy overlap, and that naming them as concretely as Death, Famine, Pestilence, etc. may be more an invention of a polytheistic culture, rather than creations of the original writer. Nonetheless, I'd call the themes War, Violence, Famine, and Death...more of a steady undoing of more and more of the world, rather than four different kinds of destruction.
Anyways, exegesis aside, I suppose it's more the "traditional" roles of the 4 horsemen that would shape a parallel mythology, and I do think that Nagash, Glottkin and Khaine work very well as Death, Pestilence/Famine and Violence. But if the chaotic violence of a civil war characterizes Khaine well, then perhaps utter conquest will be a theme for the Skaven. Any thoughts on what character will take center stage on the Skaven side of things?