Green’s Dictionary of Slang

to get a red nose through excessive drinking.

[1900		Bulletin (Sydney) 20 Oct. 13/3: He will think for himself, sings lively songs, and, alas – smokes! Smokes a pipe! In the Wesleyan compartment of the Heavenly Kingdom there is very little salvation to be found by the parson who colors a meerschaum].
1909		J. Ware Passing Eng. of the Victorian Era 86/1: Colour the meerschaum, To. Drinking to the extent of reddening the nose. ‘Aint ’e colourin’ ’is meerschaum?’ The phrase arises from an association of ideas – those in the first place of darkening the colour of a meerschaum pipe by steady smoking, and in the second, intensifying the hue of the nose by steady drinking.