The 'mare' in nightmare isn't a horse. It's a demon that sits on your chest.

Old English speakers knew exactly what was crushing them in the dark. The word 'mare' — from the Proto-Germanic *marōn — named a malevolent spirit believed to pin sleeping people to their beds, pressing the breath from their lungs. No hooves, no mane. Pure malice.
The creature appears across Germanic and Slavic traditions under close cousins of the same name: the German Mahr, the Old Norse mara, the Polish mora. Each culture described the same terrifying experience — waking unable to move, chest heavy, a presence felt but not quite seen. We now call it sleep paralysis. They called it a visitation.
When 'night' was prefixed to 'mare' in Middle English, around the 13th century, it wasn't for emphasis — nighttime was simply when the mare did its worst work. The compound stuck. The spirit eventually faded from belief, but the word kept its shape, carrying the ghost of the demon inside it.
The horse meaning of 'mare' is entirely unrelated, from a different Old English root, mēare. Centuries of casual confusion have quietly made the nightmare sound like a bad equestrian dream. It was always something heavier than that.