  We present calculations showing that upcoming Cosmic Microwave Background
(CMB) experiments will have the power to improve on current constraints on
neutrino masses and provide new limits on neutrino degeneracy parameters. The
latter could surpass those derived from Big Bang Nucleosynthesis (BBN) and the
observationally-inferred primordial helium abundance. These conclusions derive
from our Monte Carlo Markov Chain (MCMC) simulations which incorporate a full
BBN nuclear reaction network. This provides a self-consistent treatment of the
helium abundance, the baryon number, the three individual neutrino degeneracy
parameters and other cosmological parameters. Our analysis focuses on the
effects of gravitational lensing on CMB constraints on neutrino rest mass and
degeneracy parameter. We find for the PLANCK experiment that total (summed)
neutrino mass $M_{\nu} > 0.29$ eV could be ruled out at $2\sigma$ or better.
Likewise neutrino degeneracy parameters $\xi_{\nu_{e}} > 0.11$ and $|
\xi_{\nu_{\mu/\tau}} | > 0.49$ could be detected or ruled out at $2\sigma$
confidence, or better. For POLARBEAR we find that the corresponding detectable
values are $M_\nu > 0.75 {\rm eV}$, $\xi_{\nu_{e}} > 0.62$, and $|
\xi_{\nu_{\mu/\tau}}| > 1.1$, while for EPIC we obtain $M_\nu > 0.20 {\rm eV}$,
$\xi_{\nu_{e}} > 0.045$, and $|\xi_{\nu_{\mu/\tau}}| > 0.29$. Our forcast for
EPIC demonstrates that CMB observations have the potential to set constraints
on neutrino degeneracy parameters which are better than BBN-derived limits and
an order of magnitude better than current WMAP-derived limits.
