The most common and most likely answer to this crossword clue is the 10 plus 3 letter word TEN-GALLON HAT
T
E
N
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G
A
L
L
O
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H
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T
Buddy explains!
The straight part
We know that "Cowboy wears it" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cowboy wears it = ten-gallon hat.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.