By assuming that liquid droplets and ice crystals within a computational grid box grow under the same conditions, mean-field representations of mixed-phase clouds in numerical models favour a quick cloud glaciation driven by the Wegener-Bergeron-Findeisen process. Consequently, maintenance of mixed-phase states under the mean-field approximation is conditioned to external dynamical forcing, such as sufficiently strong updraughts. In this work we go beyond the mean-field representation and investigate the maintenance of mixed-phase states in adiabatic (non-entraining) cloud volumes by accounting for local variability in a particle's growth conditions in the turbulent cloud environment. This is done by using a Lagrangian microphysical scheme, where temperature and vapour mixing ratio are stochastic attributes attached to each cloud particle. Different dynamic scenarios show that microphysical variability and parametrised turbulence effects may significantly reduce cloud glaciation rates, resulting in much more resilient mixed-phase states in idealised parcels containing non-sedimenting and non-aggregating cloud particles. We have stated a more refined criterion for the Wegener?Bergeron?Findeisen process activity in the bulk of a mixed-phase cloud parcel (or computational grid box). This criterion is stated in terms of the conditional average supersaturations that are experienced by specific cloud particle types (liquid or ice), and not in terms of unconditional averages corresponding to parcel- or grid-mean values of supersaturations. Formulation of a relation between conditional and unconditional average supersaturations poses an interesting closure problem in mixed-phase cloud microphysics. Our stochastic microphysical model provides a Lagrangian closure to this problem and gives insights towards the development of a prognostic stochastic subgrid-scale scheme for condensation/deposition in numerical models of mixed-phase clouds