As a result of competing physical mechanisms, the atmospheric composition of white dwarfs changes throughout their evolution, a process known as spectral evolution. Because of the ambiguity of their atmospheric compositions and the difficulties inherent to the modeling of their dense atmospheres, no consensus exists regarding the spectral evolution of cool white dwarfs (Teff<6000K). In the previous papers of this series, we presented and observationally validated a new generation of cool white dwarf atmosphere models that include all the necessary constitutive physics to accurately model those objects. Using these new models and a homogeneous sample of 501 cool white dwarfs, we revisit the spectral evolution of cool white dwarfs. Our sample includes all spectroscopically identified white dwarfs cooler than 8300K for which a parallax is available in Gaia DR2 and photometric observations are available in Pan-STARRS1 and 2MASS. Except for a few cool carbon-polluted objects, our models allow an excellent fit to the spectroscopic and photometric observations of all objects included in our sample. We identify a decrease of the ratio of hydrogen- to helium-rich objects between 7500 and 6250K, which we interpret as the signature of convective mixing. After this decrease, hydrogen-rich objects become more abundant up to 5000K. This puzzling increase, reminiscent of the non-DA gap, has yet to be explained. At lower temperatures, below 5000K, hydrogen-rich white dwarfs become rarer, which rules out the scenario in which the accretion of hydrogen from the interstellar medium dominates the spectral evolution of cool white dwarfs.