Due to the metric expansion of space, light emitted from earlier times in faraway parts of the universe and travels for a long time to reach us get progressively redshifted, decreasing the energy of the photon. (e.g. light from faraway galaxies, cosmic microwave background radiation, etc) And the earlier and further away it was emitted, the more redshifted it becomes.
What is the analogous thing that happens to particles with rest mass (e.g. neutrinos)? When you decrease the energy of a particle with rest mass, its speed decreases. (Or looked at another way, if the thing emitting it is moving away, then the particle is traveling slower towards us relative to us.) So does that mean that particles emitted from earlier times from far away traveling through empty space to reach us get slowed down (and more slowed down the earlier and further away it came from)?
If so, could this slowing down cause neutrinos to turn from "hot dark matter" into "warm dark matter" or "cold dark matter"?