Voicing support, boss at paper protects nut like Coot? (10)

I believe the answer is:

bareheaded

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'paper protects nut like coot?' is the definition.
I can't tell whether this definition defines the answer.

'voicing support boss' is the wordplay.
'voicing' indicates a 'sounds like' (homophone) clue (I've seen 'voiced' mean this).
'support' becomes 'bear' (bear can mean to support or carry).
'boss' becomes 'headed' (I can't justify this - if you can you should believe this answer much more).
'bear' sounds like 'bare'.
'bare'+'headed'='BAREHEADED'

'at' acts as a link.

Can you help me to learn more?

(Another definition for bareheaded that I've seen is " without hat".)

I've seen this clue in The Independent.

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