Green’s Dictionary of Slang

a red nose, gained through drinking; thus, a habitual drunkard.

1959		I. & P. Opie Lore and Lang. of Schoolchildren (1977) 192: There are also, according to juvenile observers, people with ‘ferret’ noses [...] ‘cheese cutters’, and ‘Rudolphs’, that is to say red noses.
1975		A. Bleasdale Scully 172: Rudolph, y’ve got a nose like a leper’s dick.