What evidence is there that dark matter isn't one of the known types of neutrinos?
If it were, how would this be measurable?
Dark matter can be hot, warm or cold. Hot means the dark matter particles are relativistic (kinetic energy on the order of the rest mass or much higher), cold means they are not relativistic (kinetic energy much less than rest mass) and warm is in between. It is known that the total amount of dark matter in the universe must be about 5 times the ordinary (baryonic) matter to explain the CMB as measured by WMAP.
However, cold dark matter must be a very significant component of the universe to explain the growth of structures from the small fluctuations in the early universe that grew to become galaxies and stars (see this reference). Thus cold dark matter is also required to explain the currently measured galactic rotation curves.
Now, the neutrino oscillation experiments prove that neutrinos have a non-zero rest mass. However, the rest masses must still be very small so they could only contribute to the hot dark matter. The reason they can only be hot dark matter is because it is assumed that in the early hot, dense universe, the neutrinos would have been in thermal equilibrium with the hot ordinary matter at that time. Since the neutrino's rest mass is so small, they would be extremely relativistic, and although the neutrinos would cool as the universe expands, they would have still been very relativistic at the time of structure formation in the early universe. Thus, they can only contribute to hot dark matter in terms of the early growth of structure formation. [Because of the expansion of the universe since then, the neutrinos should have cooled so much that they are non-relativistic today.]
According to this source:
Current estimates for the neutrino fraction of the Universe’s mass–energy density lie in the range 0.1% <∼ ν <∼ a few %, under standard assumptions. The uncertainty reflects our incomplete knowledge of neutrino properties.
So most cosmic neutrinos are probably less than 10% of the total dark matter in the universe. In addition most of the rest (of the non-neutrino) 90% of dark matter must also be cold dark matter - both in the early universe and even now.
Hot dark matter could be partly neutrinos - but they (probably) don't interact enough to have been resposnible for initial galaxy formation.
Neutrinos from the big bang have been redshifted to ~2K = ~0.0002 eV, which is considerably lower than the current best upper bound on neutrino rest mass (0.1eV). We have no way to directly detect the flux of neutrinos at this low energy and the indirect methods at deducing it are tentative at best. So primordial neutrinos might indeed be a significant component of Cold/Warm dark matter. We don't know.
Cold neutrinos which clumped together would form a Fermi-Dirac condensate. Unlike electrons in an atom there would be no mutual repulsion and the quantum numbers could increase truly "astronomically". For a large concentrate all but the early neutrino contributors would be far from cold. Such a concentrate would behave like a huge heavy ball of unobservable, very rareified liquid which is exacty what you see in a barred spiral galaxy, the bar is in the liquid where g varies as r and the spiral arms are outside, subject to the inverse square law. Cold neutrinos may have been around since the early universe but another source could be black holes where they may pour out like Hawkinge radiation or as a result of accretion disc annihilation at the event horizon. Either way they would be very cold by the time they had crawled away from the hole.