Horses cannot breathe through their mouth. If their nostrils become obstructed, they could suffocate.
However, they could still die from having food stuck in their throats. It would keep them from swallowing, so they would be unable to drink and die from dehydration.
This is a condition called "choke". Choke can also cause ulcers and swelling. Choke happens when horses eat too quickly.
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