As far as theory goes, the Cosmic Neutrino Background (CvB) was created within the first second after the Big Bang, when neutrinos decoupled from other matter. Nevertheless, while the universe was still hot neutrinos stayed in thermal equilibrium with photons. Neutrinos and photons shared a common temperature until the universe cooled down to a point where electrons and positrons annihilated and transfered their temperature to the photons. With the continuing expansion of the universe both the photon background and the neutrino background continued to cool down.
From these assumptions one can derive the properties of the Cosmic Neutrino Background today. The calculations are neither particularly lengthy or difficult, but I'll skip them here. As a result of these calculations one expects the CvB to have a temperature of
$$ T_\nu = 1.95~\mathrm{K} = 1.7\cdot 10^{-4}~\mathrm{eV},$$
an average momentum of
$$ \left< p \right> = 5.314 \cdot 10^{-4}~\mathrm{eV},$$
a root mean squared momentum dispersion of
$$ \sqrt{\left< p^2 \right>} = 6.044 \cdot 10^{-3}~\mathrm{eV}$$
and a density of
$$ 112~\nu/\mathrm{cm}^3 $$
for each of the three neutrino flavors. This density is many orders of magnitude more abundant in that energy range than neutrinos from any other sources. This number is equally divided into neutrinos and antineutrinos.
These are rather hard predictions of Big Bang cosmology. This makes the CvB so important: if we could measure it, any deviation of these numbers cited above would mean that there is a serious and fundamental flaw in our cosmological models.
However, one has to keep in mind that all these numbers are averaged over the whole universe. Since neutrinos do have a non-zero rest mass, they are indeed affected by gravity. They cannot cluster like Dark Matter, because even though CvB Neutrinos are "slow", they are still too fast (many hundreds of km/s) to form clusters and therefore no viable Dark Matter candidate. But they may form gigantic weakly bound halos around galaxies that go far beyond the Dark Matter clusters. This may lead to a local enhancement of the CvB density due to the gravitational attraction of the massive neutrinos to large-scale structures in the universe. Unfortunately, this density enhancement cannot be quantified yet, because it depends very much on the absolute neutrino mass, which is still unknown today. For a mass of 0.1$~$eV, which you assumed in your question, there would probably be no relevant density enhancement of CvB neutrinos near our galaxy. The neutrinos would be too fast and simply stream out of the gravitational potential. If the neutrino masses turn out to be larger, on the other hand, the effect of gravity can become significant and density enhancement factors of $\approx$100 might be possible.
There would also be a "CvB neutrino wind". Just like the Cosmic Microwave Background, the neutrino background is not co-moving with our reference frame. Rather, our galaxy and the Earth are passing through the gigantic cloud of CvB neutrinos, so the neutrino distribution would not appear completely isotropic to us. It would appear a bit blue-shifted in one direction and a bit red-shifted in the other.
I would like to emphasize though, that a possible CvB detection experiment would probably not yield much information about the properties of the CvB. The only feasible method conceived to detect CvB neutrinos uses the neutrino induced $\beta$-decay of unstable nuclei. This process mainly provides us a yes/no-answer about the existence of the Cosmic Background Neutrinos. It does not tell us anything about the temperature of the CvB. In principle it would be possible to determine the density (via the rate) or even the anisotropy (via an annular rate modulation), but I doubt that it we could get anything better than the right order of magnitude. What one can determine from neutrino induced $\beta$-decay is the absolute neutrino mass. But this is not a property specific to the CvB and can be measured in other ways, too.
Best Answer
Back when I was in graduate school in the 1990s, the standard reference for this sort of thing was Kolb and Turner's book The Early Universe. Even after all these years, that book's treatment of this subject is probably still a good place to look.
Even if there's no asymmetry-producing process for neutrinos (like baryogenesis), you still expect a relic neutrino background that's a thermal (Fermi-Dirac) distribution of both neutrinos and antineutrinos, with a temperature of about 2 K. The reason is that, at a certain time in the evolution of the Universe, the density dropped low enough that the neutrino number "froze out": interactions that could change the number of neutrinos (such as primarily $e^- e^+ \leftrightarrow \nu_e\ \bar\nu_e$) became so rare that the time for any given particle to undergo such a reaction grew much longer than a Hubble time.
It's been a long time since I looked at baryogenesis models with any care, but as I recall some models would be expected to produce an asymmetry in the neutrino sector as well. But in practice I don't think that would change the prediction much. The reason is that baryogenesis only has to produce a one part in $10^9$ asymmetry (a billion and one protons for every billion antiprotons). That produces very noticeable effects today, because there was essentially complete annihilation of the antiprotons. But neutrino freeze-out occurs much earlier, while neutrinos are still relativistic, so we don't think that that massive annihilation happened for neutrinos. So even if there is a neutrino-antineutrino asymmetry comparable to the asymmetry produced by baryogenesis, it should only result in a tiny difference in the number of neutrinos over antineutrinos.
Let me put that another way. At early times, (temperature much greater than the proton mass), there were comparable numbers of photons, neutrinos, and protons. Baryogenesis resulted in an asymmetry of protons over antiprotons at that time. After that, nearly all of the protons and antiprotons annihilated, leaving the observed result that today there are a billion photons for every proton. But we expect the number of relic neutrinos to be of the same order as the number of photons, not protons, so a baryogenesis-level neutrino asymmetry won't be noticeable.