AbstractSnow on Arctic sea ice has many, contrasting effects on ice thickness and extent. Furthermore, estimates of snow depth on Arctic sea ice are a key input for ice thickness estimates from satellite altimeters such as ICESat‐2. Models such as the NASA Eulerian Snow on Sea Ice Model (NESOSIM) have been recently utilized by the sea ice community to provide time‐varying basin‐wide estimates of snow depth and density on Arctic sea ice. NESOSIM is a two‐snow‐layer model with simple representations of snow accumulation, wind packing, loss due to blowing snow, and redistribution due to sea ice motion. Two free parameters in NESOSIM, which dictate the bulk effect of wind packing (densification) and blowing snow processes, lack direct observational constraints. We present an indirect calibration of these parameters using a Markov Chain Monte Carlo (MCMC) approach. NESOSIM output is calibrated to observations of snow depth from Operation IceBridge and CRREL‐Dartmouth buoys, and density from historical drifting stations. OIB measurements alone are found to more strictly constrain the blowing snow parameter, and including additional observations yields more physically reasonable density estimates. The MCMC‐calibrated model output is further used to estimate sea ice thickness and uncertainty from model parameter uncertainty using ICESat‐2 freeboard measurements. Despite visible differences in density, the change in ice thickness is minimal. We also find that the model is relatively insensitive to parameter variations, and hence, the snow model uncertainty contribution to ice thickness is small compared to the systematic uncertainty from snow in the current ICESat‐2 thickness product.