water - What is the pH of ice?

The pH of pure liquid water depends on temperature. It is about pH = 7.0 at room temperature, pH = 6.1 at 100 °C, and pH = 7.5 at 0 °C. What happens to the pH (or to the ion product) of pure water when it freezes?

I assume that the proton transfer reactions

$$\ce{2H2O <=> H3O+ + OH-}$$ $$\ce{H3O+ + H2O <=> H2O + H3O+}$$ $$\ce{H2O + OH- <=> OH- + H2O}$$ are too fast, so that any present $\ce{H3O+}$ and $\ce{OH-}$ cannot be easily trapped in the solid ice crystal when it grows. Does that mean that pure ice crystals are free of $\ce{H3O+}$ and $\ce{OH-}$ ions?