The time-dependent process of raindrop freezing is described in a general form, including thermodynamic effects from the accretion of cloud liquid and cloud ice. Freezing drops (FDs) larger than 80 m (and their water mass) are represented explicitly in a cloud model with spectral bin microphysics. FDs consist of interior water covered by ice initially. Possibilities of both dry (icy surface) and wet growth (surface covered by liquid) of FDs are accounted for.Schemes of time-dependent freezing for rain (discussed in this paper) and wet growth of hail and graupel (discussed in Part I) were implemented in a spectral bin microphysics cloud model. The model predicted that accretion of liquid produces giant FDs of 0.5-2 cm in diameter, far larger than purely liquid drops can become. This growth of FDs is promoted by recirculation from the downdraft back into the updraft and by cessation of internal freezing from some accreted liquid remaining unfrozen (wet growth of FDs). Significant contents of FDs reach a height level of 7 km (-29 degrees C) in the simulated storm. After FDs finish freezing and become hailstones, wet growth may resume. The critical diameter separating wet- and dry-growth regimes is predicted to increase with height for FDs and is more vertically uniform for hail.A sensitivity test shows that time-dependent freezing initially delays the formation of hail but later in the mature stage of the storm boosts it. Convection is invigorated. Hail and freezing drops are upwelled to higher levels, causing hail to grow to sizes up to 100% larger than without time-dependent freezing.