Green’s Dictionary of Slang

mudding-face n.

[mud n. + play on SE pudding-face]

a fool, a weakling.

‘She Was True to Somebody Else’ [ballad] She oped the lattice, and I saw that form of queenly grace, / And heard her very softly say, ‘Good-night, old mudding-face!’.
[UK]Farmer & Henley Sl. and Its Analogues.