  We report on the search for dark matter WIMPs in the mass range below 10
GeV/c$^2$, from the analysis of the entire dataset acquired with a
low-radioactivity argon target by the DarkSide-50 experiment at LNGS. The new
analysis benefits from more accurate calibration of the detector response,
improved background model, and better determination of systematic
uncertainties, allowing us to accurately model the background rate and spectra
down to 0.06 keV$_{er}$. A 90% C.L. exclusion limit for the spin-independent
cross section of 3 GeV/c$^2$ mass WIMP on nucleons is set at
6$\times$10$^{-43}$ cm$^2$, about a factor 10 better than the previous
DarkSide-50 limit. This analysis extends the exclusion region for
spin-independent dark matter interactions below the current experimental
constraints in the $[1.2, 3.6]$ GeV/c$^2$ WIMP mass range.
