Snow on Arctic sea ice plays many, sometimes contrasting roles in Arctic climate feedbacks. Snow depth is also a key input for sea ice thickness derived from ice altimetry measurements, such as satellite lidar observations from ICESat-2. Making direct snow measurements is logistically challenging in the Arctic due to the remoteness of the region, so basin-wide snow depth on sea ice is difficult to observationally constrain, and its uncertainties are seldom quantified. Snow-on-sea-ice models, such as the NASA Eulerian Snow On Sea Ice Model (NESOSIM), can provide snow depth and density estimates over Arctic sea ice. NESOSIM includes free parameters which dictate the strength of snow densification and loss processes, but these parameters are not observationally well-constrained. This talk presents a calibration of NESOSIM free parameters to snow depth and density observations using a Metropolis Markov Chain Monte Carlo method. This method produces estimates of the free parameters and their uncertainty distributions. These estimates are propagated through NESOSIM to produce uncertainty estimates for model snow depth and density. Finally, we estimate the resulting sea ice thickness using NESOSIM output and ICESat-2 altimetry measurements, and quantify the contribution of snow uncertainty to uncertainty in sea ice thickness.