Final answer:
The word that means to pester or badger and can refer to a worthless horse is 'nag'.
Step-by-step explanation:
The 3-letter word that means to pester or badger and can also refer to a worthless horse is a) Nag. In various texts, horses that are unruly or difficult to manage are often described using terms like 'iron-jawed devil', 'unruly when he's corralled', or as having traits opposite to amiability, similar to the way the word 'nag' can be used in a figurative sense to describe persistently annoying behavior. Moreover, the word 'nag' can denote a horse that is not in good condition or is of little value, as in the excerpt where a horse with 'lamentable swollen joints' might be referred to as a nag if it is deemed worthless.