What are the four beasts of Daniel 7?
The four horses of the first four seals in Revelation 6, white, red, black and pale, represent angelic spirits of judgment that God sends into the earth to conquer, remove peace, bring famine and bring death, and Zechariah's visions of chariots and horses explain who and what they are.
When the Lamb opens the first four seals in Revelation 6, four horses come forth one after another: white, red, black and pale. Revelation 6:1-8 describes the white horse rider with a bow and a crown who goes forth conquering, the red horse rider given a great sword and power to take peace from the earth so that men kill one another, the black horse rider with a pair of balances bringing famine and high prices for wheat and barley while the oil and wine are protected, and finally the pale horse whose rider is named Death, with Hell following him, given power over a fourth of the earth to kill by sword, hunger, death and the beasts of the earth.
These horses are not left unexplained, because the book of Zechariah shows who they are. Zechariah 1:8-11 and Zechariah 6:1-8 describe four chariots with red, black, white and grisled (pale) horses coming from between two mountains of brass, and the angel explains that these are the four spirits of the heavens which stand before the Lord of all the earth and go forth to walk to and fro through it. Brass represents judgment, so these spirits are responsible for carrying out or holding back judgment on the nations. It is made clear that these are angelic spirits, not devils and not nations, which shows that the judgments men face are determined by God the Father.
Daniel 4:17 reinforces this, declaring that the decree comes from the watchers and the holy ones so that the living may know that the Most High rules in the kingdom of men and gives it to whomever He will, even setting up the basest of men. Daniel 4:35 adds that all the inhabitants of the earth are reputed as nothing before Him, and He does according to His will in the army of heaven and among men, so that none can stay His hand. This means that even the rise of a fierce and deceitful ruler in the end times, one who breaks covenant and destroys many by peace and craft, as described in Psalm 55:20-23 and Daniel 8:23-25, only happens because it is first allowed by these four horses and their riders.
So the four horsemen of the seals are pictured as agents carrying out God's ordained judgments in the earth, whether through deception, war, famine or death, and their appearing in Revelation 6 previews what will unfold later in the book through the trumpet and vial judgments, rather than being a chronological sequence of new events beginning at that point.
The scriptures
And I saw when the Lamb opened one of the seals, and I heard, as it were the noise of thunder, one of the four beasts saying, Come and see. And I saw, and behold a white horse: and he that sat on him had a bow; and a crown was given unto him: and he went forth conquering, and to conquer. And when he had opened the second seal, I heard the second beast say, Come and see. And there went out another horse that was red: and power was given to him that sat thereon to take peace from the earth, and that they should kill one another: and there was given unto him a great sword. And when he had opened the third seal, I heard the third beast say, Come and see. And I beheld, and lo a black horse; and he that sat on him had a pair of balances in his hand. And I heard a voice in the midst of the four beasts say, A measure of wheat for a penny, and three measures of barley for a penny; and see thou hurt not the oil and the wine. And when he had opened the fourth seal, I heard the voice of the fourth beast say, Come and see. And I looked, and behold a pale horse: and his name that sat on him was Death, and Hell followed with him. And power was given unto them over the fourth part of the earth, to kill with sword, and with hunger, and with death, and with the beasts of the earth.
I saw by night, and behold a man riding upon a red horse, and he stood among the myrtle trees that were in the bottom; and behind him were there red horses, speckled, and white. Then said I, O my lord, what are these? And the angel that talked with me said unto me, I will shew thee what these be. And the man that stood among the myrtle trees answered and said, These are they whom the LORD hath sent to walk to and fro through the earth. And they answered the angel of the LORD that stood among the myrtle trees, and said, We have walked to and fro through the earth, and, behold, all the earth sitteth still, and is at rest.
And I turned, and lifted up mine eyes, and looked, and, behold, there came four chariots out from between two mountains; and the mountains were mountains of brass. In the first chariot were red horses; and in the second chariot black horses; And in the third chariot white horses; and in the fourth chariot grisled and bay horses. Then I answered and said unto the angel that talked with me, What are these, my lord? And the angel answered and said unto me, These are the four spirits of the heavens, which go forth from standing before the LORD of all the earth. The black horses which are therein go forth into the north country; and the white go forth after them; and the grisled go forth toward the south country. And the bay went forth, and sought to go that they might walk to and fro through the earth: and he said, Get you hence, walk to and fro through the earth. So they walked to and fro through the earth. Then cried he upon me, and spake unto me, saying, Behold, these that go toward the north country have quieted my spirit in the north country.
This matter is by the decree of the watchers, and the demand by the word of the holy ones: to the intent that the living may know that the most High ruleth in the kingdom of men, and giveth it to whomsoever he will, and setteth up over it the basest of men.
And all the inhabitants of the earth are reputed as nothing: and he doeth according to his will in the army of heaven, and among the inhabitants of the earth: and none can stay his hand, or say unto him, What doest thou?
He hath put forth his hands against such as be at peace with him: he hath broken his covenant. The words of his mouth were smoother than butter, but war was in his heart: his words were softer than oil, yet were they drawn swords. Cast thy burden upon the LORD, and he shall sustain thee: he shall never suffer the righteous to be moved. But thou, O God, shalt bring them down into the pit of destruction: bloody and deceitful men shall not live out half their days; but I will trust in thee.
And in the latter time of their kingdom, when the transgressors are come to the full, a king of fierce countenance, and understanding dark sentences, shall stand up. And his power shall be mighty, but not by his own power: and he shall destroy wonderfully, and shall prosper, and practise, and shall destroy the mighty and the holy people. And through his policy also he shall cause craft to prosper in his hand; and he shall magnify himself in his heart, and by peace shall destroy many: he shall also stand up against the Prince of princes; but he shall be broken without hand.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.