You wake up at night sensing a weight on your legs that you thought was your pet dog – only to remember they died years ago.

Their riders' chest armor, swords and distinctive helmet, adorned with plumes of horses' hair, will be familiar to anyone who watches Britain’s opulent royal events in person or on TV.

Around the world, relationships between people and horses have had a tremendous impact on the human story, forever changing ways of life from transport to communication, subsistence, and belief.

DRUZHKIVKA, Ukraine—On the eastern front here, Russia is saddling up a mainstay of battlefields from earlier centuries to counter Ukraine’s drone army: horses and donkeys. The hoofed mammals ...