Eowyn killed the fell beast ridden by the Witch-King by cutting off its head. If it were a dragon this would not have been possible as dragons had strong scales that served as armour over their whole body, except their bellies. If it was a dragon, her sword would've just bounced off. I think Tolkien said in one of his letters that the fell beasts were a pterosaur like creature.
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His sword was long his lance was keen
His shining helm afar was seen
The countless stars of heavens field
Were mirrored in his silver shield
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