The overall appearances of the horses on different occasaions/events collectively represent the innocent deaths, the chaos, fall of Batman, the rise of Doomsday, Superman's death etc.
This is explained nicely by the user delarozay on 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.