Os cavalos possivelmente representam os Quatro Cavaleiros do Apocalipse .As aparições gerais dos cavalos em diferentes Ocasiões / Eventos representam coletivamente as mortes inocentes, o caos, a queda do Batman, a ascensão do Dia do Juízo Final, a morte do Super-Homem, etc.
Isso é explicado muito bem pelo usuário delarozay no Reddit :
Basically the 4 horseman (or horses) of the Apocalypse symbolize the end of times, so I just interpreted the first 4 appearances of horses as the build up to the end. If the 4th horse was in fact the one that was shown after the bomb went off then it makes sense as that would be when it all comes apart. Innocent people die, Doomsday is created, end of times as prophesied. However there probably is a deeper meaning behind each of the times they're shown.
The first horseman of the Apocalypse is mentioned in Revelation 6:2: “I looked, and there before me was a white horse! Its rider held a bow, and he was given a crown, and he rode out as a conqueror bent on conquest.” - The 1st horse we see crosses Bruce's path so this passage ties well with Batman.
The second horseman of the Apocalypse appears in Revelation 6:4, “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.” - The 2nd horse is shown in Lex Luthor's home, he's our villain and the passage fits him perfectly.
The third horseman is described in Revelation 6:5-6, “...and there before me was a black horse! Its rider was holding a pair of scales in his hand... - The 3rd horse is shown on the wallpaper while Clark & Bruce are speaking with each other ("pair of scales").
The fourth horseman is mentioned in Revelation 6:8, “I looked, and there before me was a pale horse! Its rider was named Death, and Hades was following close behind him. They were given power over a fourth of the earth to kill by sword, famine and plague, and by the wild beasts of the earth.” - The 4th horse is shown after the explosion in the courthouse where at this point in the film we reach our boiling point.