The character in this 1700's rhyme, lived on the moon, and had an unusual style of dress.
Who was he? And what musical instrument did he play?

That would be Aiken Drum and despite his surname it was a 'ladle' he played upon.

Aiken Drum

Viv

Well done Viv,
Aiken Drum was an Primary School favourite when I was growing up:

Nursery Rhyme Origins and Lyrics:

Aiken Drum
There was a man lived in the moon,
Lived in the moon, lived in the moon
There was a man lived in the moon,
And his name was Aiken Drum.

Chorus

And he played upon a ladle,
a ladle, a ladle
And he played upon a ladle,
and his name was Aiken Drum.

And his hat was made of good cream cheese,
of good cream cheese, of good cream cheese,
And his hat was made of good cream cheese
And his name was Aiken Drum.

Chorus

And his coat was made of good roast beef,
of good roast beef, of good roast beef,
And his coat was made of good roast beef,
And his name was Aiken Drum.

Chorus

And his buttons made of penny loaves,
of penny loaves, of penny loaves,
And his buttons made of penny loaves,
And his name was Aiken Drum.

Chorus

And his breeches made of haggis bags
of haggis bags, of haggis bags
And his breeches made of haggis bags,
and his name was Aiken Drum.


And from your Wikipedia link:
The rhyme originates from Scotland, likely going back to the Jacobite Rising of 1715. Aiken Drum was possibly a Brownie; a mischevious elf.
As with many traditional folk songs, the words and music have changed over the years. More modern versions of the rhyme have Aiken Drum's hair made of spaghetti, and meatballs for eyes.