Having a hard time finding those pesky horses? Here's a guide to show you how to find them!
It's quite simple actually! Just takes some time and patients!

The Harbinger will ask you to 'visit the dens of other kings'.
This means you will need to search other players' dens to look for them.
It may take you one try, or 100 tries. Just don't give up!
They're not hard to miss. Once found, they will appear at the very top of the den page.
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The first Horse of the Apocalypse is the White Horse of Pestilence.

"You see the horse off in the distance. A loud shriek tears through the air, causing every hair on your body to stand up. You have witnessed a new Omen. This king's lands have been defiled by the White Horse of Pestilence. Its hooves clatter at the ground, and with every step, swarms of locust, flies, and toxic clouds of air arise. You mark this location for the Harbinger."
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The second Horse of the Apocalypse is the Red Horse of War.

"You see the horse off in the distance. A beastly roar rumbles through the ground, sending tremors of fear throughout your body. You have witnessed a new Omen. This king's lands have been depraved by the Red Horse of War. Its hooves clatter at the ground, and as it passes, all living creatures in its path turn against one another in a bloody battle to the death. You mark this location for the Harbinger."
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The third Horse of the Apocalypse is the Black Horse of Famine.

"You see the horse off in the distance. A wailing cry of death rips through the air, chilling every bone in your body. You have witnessed a new Omen. This king's lands have been devastated by the Black Horse of Famine. Its hooves clatter at the ground, and as it runs through the fields, carrion birds, hyenas, and jackals consume every ounce of food to be found, leaving the lands barren of life. You mark this location for the Harbinger."
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Last, the fourth Horse of the Apocalypse is the Pale Horse of Death.

"You see the horse off in the distance. Its silence is even more unnerving than the cries of its cohorts; your blood runs cold. You have witnessed a new Omen. This king's lands have been desecrated by the Pale Horse of Death. It walks slowly, and as it passes, every living being in its wake withers and dies. A white trail of smoke evaporates from the animals and plants that have been destroyed, turning the world to a bleak ashen colour as it all begins to crumble away. You mark this location for the Harbinger."
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In Explore, you may encounter this:

"A Horse of the Apocalypse can be seen running on the horizon among ruins, just before disappearing into a vortex. You were too far away to notice which horse it was."

This is only an Omen and does NOT count towards seeing one of the Four Horses! You can only find them on other player's dens.

I hope this clears up alot of confusion a helps others progress forward! Good luck!