Interestingly, the phrase "four horsemen of the apocalypse" is not found in the King James Bible! It is merely a shorthand way of referring to 4 horses and their riders who appear when Jesus opens the first four of seven prophetic seals.
The 4 seals Jesus opens correlate to the global disasters he discussed in his famous Mount Olivet prophecies (Matthew 24, Luke 21, Mark 13). Each of the four horsemen represents a calamity that comes upon the earth as a precursor to the dreaded Day of the Lord when God's wrath against sin is manifested.
Why Horses?
Horses in the Bible were used primarily to wage war (see Exodus 14:9, Deuteronomy 17:14 - 16, etc.). Their selection in Revelation symbolizes the war-like and fast-paced opposition to humanity their riders represent.
Why Four?
Why are there four horsemen related to the apocalypse and not two or seven? The modern phrase "four corners of the earth," taken from Isaiah 11:12, is also used in Revelation 7:1. It alludes to the primary directions on a compass. These 4 distinct riders were likely used to symbolize the global nature of the curses they bring.
The First Rider
This first of four riders, possessing a bow and a crown, rides a white horse. His crown symbolizes his authority to conquer (Revelation 6:2). Jesus himself, like the three horsemen that will follow, reveals what this first symbol represents.
Be on guard, so that no one deceives you. For many shall come in My name, saying, 'I am the Christ'; and they shall deceive MANY . . . (Matthew 24:4 - 5, see also verses 11, 24).
This first of four horsemen of the apocalypse represents deception (especially religious) on a grand scale. His bloodless ride symbolizes the conquering of human hearts through lies and deceit. Satan's greatest trick is to appear to represent righteousness. His goal, however, is to subvert anyone he can into obeying and worshipping him instead of the true God (2Corinthians 11:13 - 15, 2Thessalonians 2:3 - 4).
The Second Rider
The second horsemen, who has the authority to take away peace from the earth (Revelation 6:4), rides a red horse. He represents war, and his actions cause people to kill one another.
And you shall hear of wars and rumors of wars . . . For nation shall rise against nation, and kingdom against kingdom . . . (Matthew 24:6 - 7, see also verse 9).
Deception on a massive scale will lead to conflict and fighting among humans. The devil's lies will accentuate human nature's tendency toward self-righteous beliefs and prejudiced thinking. The manifold reasons humans create to justify their superiority over others will lead to bloodshed worldwide.
The Third Rider
The third of four horsemen has a balance in his hand and rides a black colored horse. A voice in the midst of four spiritual creatures cries, "A measure of wheat for a silver coin, and three measures of barley for a silver coin . . ." (Revelation 6:5 - 6).
The parallel account in Jesus' Olivet prophecies states that, ". . . and there shall be famines and pestilences and earthquakes in different places" (Matthew 24:7).
The third of four horsemen represents famine that brings hunger and starvation. A silver coin was considered a day's wages for a laborer. These verses tell us that humans, in the end time, will have to work a full day just to buy food to sustain themselves a little longer. Famine is a natural consequence of war.
The Last Horsemen
The fourth of the four horsemen of the apocalypse rides a horse that many Bibles state is pale. Its color, however, is more likely pale green or greenish. The Greek word from which the translations derive "pale" is chloros (Strong's #G5515) which clearly refers to green (Mark 6:39, Revelation 8:7, 9:4). The rider of this horse is Death, the only one of the four who has a name (Revelation 6:8).
Why is the horse of this fourth horsemen a greenish pale? It is because it symbolizes death, as people with lighter skin usually appear pale (greenish) within 15 to 25 minutes after life ends. This change is caused by blood leaving the skin surface due to the circulatory system shutting down.
The rider is granted authority to kill 25% of the earth's population (Revelation 6:8). His is the biggest "harvest" of dead humans up to this point in prophecy. Jesus stated that unless he returned all human life would cease to exist (Matthew 24:21 - 22).
Conclusion
Why does God allow the four horsemen of the apocalypse to ride? It is because, in the End Time, human hearts will have become so hard against Him that it will take the suffering they bring to begin to soften them. This softening will lead to repentance (Revelation 7).