Mixed-phase clouds greatly affect projections of future climate, with recent evaluations highlighting the influence of the ice nucleation process in these clouds. Here we explore how this process affects climate sensitivity using simulations of the Community Earth System Model version 2 (CESM2). Ice nucleation is found to influence simulated cloud feedbacks not just over extratropical low clouds but over most regions and levels of the troposphere. However, the otherwise major influence of ice nucleation on total cloud feedback is negated when holding global mean cloud phase to observed levels. In satellite-constrained model experiments, dissimilar ice nucleation realizations all result in a strongly positive total cloud feedback, as in the default model. Global-scale cloud phase is hence confirmed to be the dominant link between ice nucleation and climate sensitivity. Conversely, whether ice nucleation is treated as aerosol-sensitive is found to be of limited importance. A microphysics update from CESM1 to CESM2 had substantially weakened ice nucleation in mixed-phase clouds, in part due to a model issue. Our findings suggest that this contributed to increased climate sensitivity primarily by reducing a global-scale cloud phase bias. Despite the issue, CESM2's ice nucleation appears to form more realistic mixed-phase clouds than either a corrected implementation or CESM1's ice nucleation scheme.