We have investigated deuteron-deuteron fusion induced by impact of (${\mathrm{D}}_{2}$O${)}_{\mathit{n}}^{+}$ and (${\mathrm{H}}_{2}$O${)}_{\mathit{n}}^{+}$ clusters with n=1\char21{}150 on deuterated polyethylene targets at energies of 135\char21{}225 keV. Both the energy dependence and magnitude of the fusion yield measured with (${\mathrm{D}}_{2}$O${)}_{115}^{+}$ clusters confirm the results of Beuhler et al. [J. Phys. Chem. 94, 7665 (1990)]. Furthermore, we have observed that the size dependence of the (${\mathrm{D}}_{2}$O${)}_{\mathit{n}}^{+}$ fusion yields measured at the impact energy of 225 keV for small (n10) clusters follow the ``thermonuclear'' model proposed by Carraro et al. [Phys. Rev. A 42, 1379 (1990)] rather than the thick-target model. For ${\mathrm{H}}_{2}$${\mathrm{O}}^{+}$ and (${\mathrm{H}}_{2}$O${)}_{2}^{+}$ at 225 keV, the yields roughly agree with the ``knock-on'' model by Carraro et al. No fusion event was observed for (${\mathrm{H}}_{2}$O${)}_{\mathit{n}}^{+}$ clusters with n=4\char21{}50; however, n=115 clusters produced an observable fusion rate. The ratio between fusion rates of (${\mathrm{H}}_{2}$O${)}_{115}^{+}$ and (${\mathrm{D}}_{2}$O${)}_{115}^{+}$ is 5%\ifmmode\pm\else\textpm\fi{}2%, in close agreement with the result, \ensuremath{\sim}5%, measured by Beuhler et al. at 300 keV.