The Mare in nightmare is not a female horse, but a Mara, an Anglo-Saxon & Old Norse term for a demon that sat on sleepers' chests, causing them to have bad dreams.
She is a common belief in Germanic folklore, and appears in many different shapes.
The Scandinavian words for Nightmare, are:
Norwegian – Mareritt
Danish – Mareridt
Swedish – Mardröm
Anglo-Saxon & Icelandic - Martröð
German - Alpdruck or Alptraum
English - Nightmare