Jamieson, Fausset and Brown on Revelation 6:4

4. red--the color of blood. The color of the horse in each case answers to the mission of the rider. Compare Mt 10:24-36, "Think not I am come to send peace on earth; I came not to send peace, but a sword." The white horse of Christ's bloodless victories is soon followed, through man's perversion of the Gospel, by the red horse of bloodshed; but this is overruled to the clearing away of the obstacles to Christ's coming kingdom. The patient ox is the emblem of the second living creature who, at the opening of this seal, saith, "Come." The saints amidst judgments on the earth in patience "endure to the end."

that they should kill--The Greek is indicative future, "that they may, as they also shall, kill one another."