  The 21-cm signal from the epoch of cosmic dawn prior to reionization consists
of a promising observable to gain new insights into the dark matter (DM)
sector. In this paper, we investigate its potential to constrain mixed (cold +
non-cold) dark matter scenarios that are characterised by the non-cold DM
fraction ($f_{\rm nCDM}$) and particle mass ($m_{\rm nCDM}$). As non-cold DM
species, we investigate both a fermionic (sterile neutrino) and a bosonic
(ultra-light axion) particle. We show how these scenarios affect the global
signal and the power spectrum using a halo-model implementation of the 21-cm
signal at cosmic dawn. Next to this study, we perform an inference-based
forecast study based on realistic mock power spectra from the Square Kilometre
Array (SKA) telescope. Assuming inefficient, yet non-zero star-formation in
minihaloes (i.e. haloes with mass below $10^8$ M$_{\odot}$), we obtain
stringent constraints on both $m_{\rm nCDM}$ and $f_{\rm nCDM}$ that go well
beyond current limits. Regarding the special case of $f_{\rm nCDM}\sim 1$, for
example, we find a constraint of $m_{\rm nCDM}>15$ keV (thermal mass) for
fermionic DM and $m_{\rm nCDM}>2\times10^{-20}$ eV for bosonic DM. For the
opposite case of dominating cold DM, we find that at most one percent of the
total DM abundance can be made of a hot fermionic or bosonic relic. All
constraints are provided at the 95 percent confidence level.
