The effects of spin polarization on the slowing down of neutrons in water is investigated. Spin-dependent scattering cross sections are derived from a combination of resonance parameters, experimental phase shifts, and optical model calculations. It is shown that the effect of polarization on the age of neutrons slowing down from an unpolarized plane source in an infinite moderator may be rigorously obtained from the P-1 approximation to the transport equation. One finds that the age of fission neutrons slowing down in water would be decreased by 0.8% by polarizing collisions with oxygen below 2.6 MeV were it not for depolarizing collisions with hydrogen that reduce this figure to 0.2%.