It is argued that the multiplicity distribution in hadron-nucleus scattering should obey universal Koba-Nielsen-Olesen scaling at each impact parameter. For the whole nucleus, scaling remains approximately valid, but universality breaks down. The model predicts that as A increases, the peak of the scaled multiplicity distribution shifts towards smaller values of n/n\ifmmode\bar\else\textasciimacron\fi{}, and the normalized dispersion and skewness increase. All these properties are in agreement with data.