The description and analysis of compound extremes affecting mid- and high latitudes in the winter requires an accurate estimation of snowfall. This variable is often missing from in situ observations and biased in climate model outputs, both in the magnitude and number of events. While climate models can be adjusted using bias correction (BC), snowfall presents additional challenges compared to other variables, preventing one from applying traditional univariate BC methods. We extend the existing literature on the estimation of the snowfall fraction from near-surface temperature, which usually involves binary thresholds or nonlinear least square fitting of sigmoidal functions. We show that, considering methods such as segmented and spline regressions and nonlinear least squares fitting, it is possible to obtain accurate out-of-sample estimates of snowfall over Europe in ERA5 reanalysis and to perform effective BC on the IPSL_WRF high-resolution EURO-CORDEX climate model when only relying on bias-adjusted temperature and precipitation. In particular, we find that cubic spline regression offers the best tradeoff as a feasible and accurate way to reconstruct or adjust snowfall observations, without requiring multivariate or conditional bias correction and stochastic generation of unobserved events.