As others have mentioned, horse teeth and jaws aren’t really designed to bite through flesh and bone, so biting “off” a finger would be unusual in the extreme.
What to do if a horse bites you?
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How to help a horse that bites when you go into the stable with it
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Can a horse bite break bones?
Horses bite to defend themselves or to express irritation and impatience. Some are sneaky and disrespectful. Horses that get pushy about being fed treats can become demanding and bite fingers and arms. Horses can bite hard enough to break fingers and can cause severe bruising and cuts.
Can you feel a horsefly bite?
Healthline described a horsefly bite as causing a “sharp, burning sensation”. “It’s common to experience itchiness, inflammation, and swelling around the bite area. You may even develop a bruise.” However, despite short-term pain, the bites generally “aren’t harmful to humans”, they continued.
Why do horses bite themselves?
Horses frequently bite each other when they are playing, and occasionally nip at their own legs or flanks to chase away flies or to signal discomfort from colic. When a horse repeatedly nips or bites himself, often to the point of drawing blood, this behavior is known as self-mutilation.