  We study the impact of assumptions about neutrino properties on the
estimation of inflationary parameters from cosmological data, with a specific
focus on the allowed contours in the $n_s/r$ plane. We study the following
neutrino properties: (i) the total neutrino mass $ M_\nu =\sum_i m_i$; (ii) the
number of relativistic degrees of freedom $N_{eff}$; and (iii) the neutrino
hierarchy: whereas previous literature assumed 3 degenerate neutrino masses or
two massless neutrino species (that do not match neutrino oscillation data), we
study the cases of normal and inverted hierarchy. Our basic result is that
these three neutrino properties induce $< 1 \sigma$ shift of the probability
contours in the $n_s/r$ plane with both current or upcoming data. We find that
the choice of neutrino hierarchy has a negligible impact. However, the minimal
cutoff on the total neutrino mass $M_{\nu,{min}}=0 $ that accompanies previous
works using the degenerate hierarchy does introduce biases in the $n_s/r$ plane
and should be replaced by $M_{\nu,min}= 0.059$ eV as required by oscillation
data. Using current CMB data from Planck and Bicep/Keck, marginalizing over $
M_\nu$ and over $r$ can lead to a shift in the mean value of $n_s$ of
$\sim0.3\sigma$ towards lower values. However, once BAO measurements are
included, the standard contours in the $n_s/r$ plane are basically reproduced.
Larger shifts of the contours in the $n_s/r$ plane (up to 0.8$\sigma$) arise
for nonstandard values of $N_{eff}$. We also provide forecasts for the future
CMB experiments COrE and Stage-IV and show that the incomplete knowledge of
neutrino properties, taken into account by a marginalization over $M_\nu$,
could induce a shift of $\sim0.4\sigma$ towards lower values in the
determination of $n_s$ (or a $\sim 0.8\sigma$ shift if one marginalizes over
$N_{eff}$). Comparison to specific inflationary models is shown.
