High level electronic structure calculations have been used to investigate the mechanism of hydrolysis of dinitrogen peroxide in small neutral water clusters containing one to six solvating water molecules. The calculations clarify some of the current uncertainties in the hydrolysis mechanism. Increasing the size of the solvating water cluster leads to strong polarization and distortion of the N2O5 entity producing incipient (but not preexisting) NO2+, thus enhancing the electrophilicity of the nitrogen atom. The reaction mechanism involves nucleophilic attack of H2O on strongly ionized N2O5 followed by proton transfer to a neighboring water and does not involve the H2ONO2+NO3- ion pair. The solvating waters actively participate in the hydrolysis mechanism. The hydrolysis products, molecular nitric acid (HONO2) and ionized (H3O+NO3-) nitric acid are found to be stable in two different types of structures containing five and six water molecules. For the cluster containing six water molecules, which has a structure related to ice, N2O5 is hydrolyzed to yield H3O+NO3- and HONO2 with essentially no barrier. The calculations thus predict, that the hydrolysis of N2O5 on PSC ice aerosols can proceed spontaneously in small neutral water clusters. Implications for heterogeneous stratospheric chemistry are discussed.