When clouds form they could become ice clouds or water clouds, which should depend mainly on temperature/altitude. There would be a transition region where the clouds could be mixed phase. Depending how much of the clouds are mixed phase and how long they remain in a mixed phase, the transition could be negligible or not. Then whether or not some additional treatment other than classical cloud condensation/nucleation models is need really depends on how much mixed phase clouds impact model precision.
I like referencing masters and doctoral theses because the candidates generally explain things in greater depth.
"This sensitivity of climate models to mixed-phase cloud specification has been confirmed by other papers; Senior and Mitchell (1993) used 4 different cloud schemes in a GCM and this gave values for the climate sensitivity parameter, λ, between 0.45 and 1.29 ◦C (W m−2)−1. It was also reported that the simulation with the cloud water scheme had a negative cloud feedback as temperature increased as less cloud water was in the ice phase and therefore did not precipitate. This effect was further increased when an interactive radiation scheme was included that treated liquid and ice cloud separately (Senior and Mitchell, 1993). Also, by changing the range of temperature in which mixed-phase clouds can exist significantly changed the radiation budget (Gregory and Morris, 1996). GCMs are also sensitive to the cloud altitude and how the liquid and ice are assumed to be mixed within the cloud as the cloud albedo is very dependent on the phase of the cloud condensate (Sun and Shine, 1994, 1995)."
From the Thesis of Andrew Barrett at the University of Reading in the UK. It would appear that the impact of mixed phase clouds is significant enough to consider.
The mixed phase clouds tend to be liquid topped producing a super saturated water radiant surface at a colder temperature while the ice particles fall below the super saturated liquid top. Unexpectedly, these mixed phased clouds can persist for many hours and potentially days at colder temperatures than "classical" treatments would indicate.
This issue by the way is the reason this blog exists. When I first noted the discrepancies in the Keihl and Trenberth Earth Energy Budgets, the missing energy was due to clouds reducing the 40 Wm-2 atmospheric window to about 22 Wm-2 or an 18 Wm-2 error compared to a potential 3.7 Wm-2 "forcing". It should be so obvious it cannot be ignored, but never underestimate how stubborn academics can be.
webster, the king of stubborn, writes this, "In the text, they applied the theory of Bose-Einstein statistics to model the condensation (8.2.3) and freezing (8.3.2) nucleation rates of water vapor. Their theory competes with the classically described mechanism that occurs in the creation of clouds, which is a nucleation of water vapor into water droplets (low clouds such as cumulus) or ice crystals (high altitude clouds such as cirrus)." That is in his appropriately titled Crackpots Etc. post. He must think that ignoring the problem of mixed phase clouds and slinging insults will make them disappear.