Dirac and Weyl semimetals display a host of novel properties. In ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$, the Dirac nodes lead to a protection mechanism that strongly suppresses backscattering in a zero magnetic field, resulting in ultrahigh mobility ($\ensuremath{\sim}{10}^{7}\text{ }\text{ }{\mathrm{cm}}^{2}\text{ }{\mathrm{V}}^{\ensuremath{-}1}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$). In an applied magnetic field, an anomalous Nernst effect is predicted to arise from the Berry curvature associated with the Weyl nodes. We report the observation of a large anomalous Nernst effect in ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$. Both the anomalous Nernst signal and transport relaxation time ${\ensuremath{\tau}}_{\mathrm{tr}}$ begin to increase rapidly at $\ensuremath{\sim}50\text{ }\text{ }\mathrm{K}$. This suggests a close relation between the protection mechanism and the anomalous Nernst effect. In a field, the quantum oscillations of bulk states display a beating effect, suggesting that the Dirac nodes split into Weyl states, allowing the Berry curvature to be observed as an anomalous Nernst effect.