The invisible horse-like creatures that pull the Hogwarts carriages are called Thestrals. They are skeletal, winged creatures with long bodies, leathery wings, clawed feet, and dragon-like faces, although most witches and wizards cannot see them.
Thestrals become important at the start of Harry Potter and the Order of the Phoenix. Harry sees them after witnessing Cedric Diggory’s death, while Harry’s friend Luna Lovegood can already see them. The books explain that a person must have seen and understood death before being able to perceive a Thestral; simply attending a funeral is not necessarily enough.
At Hogwarts, a herd of Thestrals pulls the carriages that carry students between the railway station at Hogsmeade and the castle. The creatures are not automatically hostile, but Hagrid explains that they can be dangerous if provoked and have a strong sense of smell for carrion and fresh meat.
They are often confused with unicorns, hippogriffs, or Abraxan horses. Those creatures may be magical mounts, but none matches the distinctive combination of invisibility, skeletal appearance, wings, and connection with witnessed death associated with Thestrals.