Most of the dark matter in the Universe is cold or nonrelativistic which rules out neutrinos as dark matter candidate as they are hot or relativistic. But why do physicists think that the dark matter is cold? How cold (i.e., how heavy) do these dark matter particles have to be?
Perhaps is instructive to know why we call it cold dark matter, and why prefer it over warm or even hot dark matter. The term refers to the velocity of the particles after decoupling. It is intuitive that it is more difficult to form a gravitationally bound structure if the particles that form it move too fast. Lower thermal velocities of dark matter particles imply that structures can grow in size after they decouple from the radiation field, way before recombination. You can picture it like this:
- There are primordial seed perturbations in the density field
- If the DM particles are cold, they are slow so the these perturbations can start growing (once decoupled from expansion) even during the epoch in which baryons are still strongly coupled to radiation
- Only after recombination, baryons are able to cool down, but at that point the seed perturbations are large enough to become potential wells (dark matter halos) to baryons to settle in (dark matter halos).
Then small halos merge together to form larger ones, and so on. The result is then galaxies form smaller, and grow by mergers. This is what we call the CDM galaxy formation model.
Now compare this to a case in which DM particles are hot. Since they diffuse (Silk Damping) easier, you need larger structures as seeds. So in this picture galaxies start large, and fragment over time.
Which is one do we observe? We just need to count galaxies, turns out that CDM works best. Since dark matter halos form and grow early, baryons quickly fall into them, which results in efficient galaxy formation, efficient enough to be consistent with today's observations. Based on this you can put constraints on the mass of the dark matter particles.
For example, by counting the number of small galaxies around the Milky Way (dwarf galaxies) we can come up with a constraint on the mass of the DM. There's a problem though, small galaxies are very difficult to observe, ruling out warm dark matter has turned out to be not that easy. Well IMHO evidence points towards CDM, but you can find plenty of literature arguing in favor of WDM, here is one example.