  From the current cosmological observations of CMB and nuclear abundances we
show, with an analytic procedure, that the total effective number of extra
neutrino species $\Delta N_{\nu}^{\rm tot}< 0.3$. We also describe the possible
signatures of non standard effects that could be revealed in future CMB
observations. This cosmological information is then applied to neutrino mixing
models. Taking into account the recent results from the SNO and SuperKamiokande
experiments, disfavouring pure active to sterile neutrino oscillations, we show
that all 4 neutrino mixing models, both of 2+2 and 3+1 type, lead to a full
thermalization of the sterile neutrino flavor. Moreover such a sterile neutrino
production excludes the possibility of an electron neutrino asymmetry
generation and we conclude that $\Delta N_{\nu}^{\rm tot}\simeq 1$, in
disagreement with the cosmological bound. This result is valid under the
assumption that the initial neutrino asymmetries are small. We suggest the
existence of a second sterile neutrino flavor, with mixing properties such to
generate a large electron neutrino asymmetry, as a possible way out.
