It is a contraction of the phrase "do on", as in "to do on a hat". Attitudes can also be donned.
From germanic, 'garbare' meaning, 'to please'
"The Sailor Who Fell From Grace With the Sea", English translation, 1965
Used mainly by office workers during lunchtime
I cut down trees, I skip and jump, I like to press wild flowers. I put on women's clothing, And hang around in bars.