  We present forecasts on cosmological parameters for a CMB-HD survey. For a
$\Lambda$CDM + $N_{eff}$ + $\sum m_\nu$ model, we find $\sigma(n_s) = 0.0013$
and $\sigma(N_{eff}) = 0.014$ using CMB and CMB lensing multipoles in the range
of $\ell \in [30, 20000]$, after adding anticipated residual foregrounds,
delensing the acoustic peaks, and adding DESI BAO data. This is about a factor
of two improvement in ability to probe inflation via $n_s$ compared to
precursor CMB surveys. The $N_{eff}$ constraint can rule out light thermal
particles back to the end of inflation with 95% CL; for example, it can rule
out the QCD axion in a model-independent way assuming the Universe's reheating
temperature was high enough that the axion thermalized. We find that delensing
the acoustic peaks and adding DESI BAO tightens parameter constraints. We also
find that baryonic effects can bias parameters if not marginalized over, and
that uncertainties in baryonic effects can increase parameter error bars;
however, the latter can be mitigated by including information about baryonic
effects from kinetic and thermal Sunyaev-Zel'dovich measurements by CMB-HD. The
CMB-HD likelihood and Fisher estimation codes used here are publicly available;
the likelihood is integrated with Cobaya to facilitate parameter forecasting.
