Results are presented from an intercomparison of single-column and cloud-resolving model simulations of a cold-air outbreak mixed-phase stratocumulus cloud observed during the Atmospheric Radiation Measurement (ARM) programme's Mixed-Phase Arctic Cloud Experiment. The observed cloud occurred in a well-mixed boundary layer with a cloud-top temperature of − 15 °C. The average liquid water path of around 160 g m−2was about two-thirds of the adiabatic value and far greater than the average mass of ice which when integrated from the surface to cloud top was around 15 g m−2. Simulations of 17 single-column models (SCMs) and 9 cloud-resolving models (CRMs) are compared. While the simulated ice water path is generally consistent with observed values, the median SCM and CRM liquid water path is a factor-of-three smaller than observed. Results from a sensitivity study in which models removed ice microphysics suggest that in many models the interaction between liquid and ice-phase microphysics is responsible for the large model underestimate of liquid water path. Despite this underestimate, the simulated liquid and ice water paths of several models are consistent with observed values. Furthermore, models with more sophisticated microphysics simulate liquid and ice water paths that are in better agreement with the observed values, although considerable scatter exists. Although no single factor guarantees a good simulation, these results emphasize the need for improvement in the model representation of mixed-phase microphysics.