Low-energy $(5--250\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ electron-stimulated desorption (ESD) has been used to study the production and removal of ${\mathrm{H}}^{+}$, $\mathrm{H}_{2}{}^{+}$, and ${\mathrm{H}}^{+}{({\mathrm{H}}_{2}\mathrm{O})}_{n=1--8}$ from porous amorphous solid water (PASW), amorphous solid water (ASW), and crystalline (CI) water ice films. The threshold energies for ESD of ${\mathrm{H}}^{+}$ and $\mathrm{H}_{2}{}^{+}$ from CI and ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^{+}({\mathrm{H}}_{2}\mathrm{O})$ from both PASW and ASW are $\ensuremath{\sim}22\ifmmode\pm\else\textpm\fi{}3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. There is also a $\mathrm{H}_{2}{}^{+}$ yield increase at $\ensuremath{\sim}40\ifmmode\pm\else\textpm\fi{}3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and a $\ensuremath{\sim}70\ifmmode\pm\else\textpm\fi{}3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ threshold for ESD of ${\mathrm{H}}^{+}{({\mathrm{H}}_{2}\mathrm{O})}_{n=2--8}$ for all phases of ice. $\mathrm{H}_{2}{}^{+}$ production and desorption involves direct molecular elimination and reactive scattering of an energetic proton. Both of these channels likely involve localized two-hole one-electron and∕or two-hole final states containing $4{a}_{1}$, $3{a}_{1}$, and∕or $2{a}_{1}$ character. The $70\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ cluster ion threshold implicates either an initial $(2a_{1}{}^{\ensuremath{-}2})$ state localized on a monomer or the presence of at least two neighboring water molecules each containing a single hole. The resulting correlated two-hole or two-hole, one-electron configurations are localized within a complex and result in an intermolecular Coulomb repulsion and cluster ion ejection. The ${\mathrm{H}}^{+}{({\mathrm{H}}_{2}\mathrm{O})}_{n}$ yields are highest from PASW relative to ASW and CI and decrease with temperature, whereas the $\mathrm{H}_{2}{}^{+}$ yields are highest for CI and increase with temperature. The temperature effects and cluster ion distributions are accounted for by distance and temperature dependent hole screening. Changes in screening, hole lifetimes and hopping probabilities are greatest for ${a}_{1}$ levels. This is supported by valence band photoemission studies of ice as a function of temperature.