This page talks about how the Bible and Christianity was brought in to the movie version when it wasn't in the book:
The Four Horsemen
The film’s visual highlight is its introductory narration and accompanying animation. In an amazingly beautiful and period-appropriate animation the background of the ‘virulent and abominable plague’ is told by Mr Bennet to his daughters. Undead rose by the millions, and ‘even the four horsemen of the apocalypse are said to have ascended from hell.’ An innocent enough turn of phrase, were it not that this seems to be exactly what has happened. Three times in the film we will see the four zombie horsemen of the apocalypse. Sadly this intriguing reading of Revelation 6 seems to have ended up on the cutting room floor, as references abound but nothing is developed.
Fortunately, though the horsemen are missing, about an hour in the theology of Pride + Prejudice + Zombies hits full swing. Lizzie Bennet (running through the forest to avoid the matrimonial desires of Mr Parson Collins) sees four dark figures in top hats. At that exact moment she ‘just happens’ to run into Lieutenant Wickham
So unfortunately, within PPZ, it is not revealed.
However, there was a sequel written, which refers to them as the traditional Biblical horsemen: war, pestilence, etc
Pride and prejudice: dreadfully ever after
Somewhere in the city, Pestilence was raising an army for its fellow horseman, Death.
I have not read PPZ: DEA, there might be a little more information, but so far it seems they've come straight out of hell.