I'm sure not, in case you don't get a response by then. I've never heard of leaving material in the alcohol when freezing post-extraction.
The cooling, as described so far, is for two separate steps... the first is for the extraction itself as the resin dissolves into the solvent. The second cooling step is for the winterizing (separating out the fats).
I'll be taking the winterizing step even further... instead of just visually identifying the fat layer when the cold solvent is poured off (which is perfectly legit to do), I'll be pouring it into a vacuum buchner filter that pulls the solvent down through 10 micron filter paper... the fats are what is left on top after the liquid drains down through. The vacuum is needed because when a filter is less than 20 microns gravity alone isn't enough "push" to get it through... imagine waiting days for it to driiiiiiiiiiiiiiip driiiiiiiiiiiiiiip! ugh
Cold is absolutely paramount if you want to remove fats... at any time if the temp goes up the fats will simply redissolve and not get trapped. That's why gr stressed to cool tools as well.
Why the buchner filter step? I have a vacuum pump anyway, because I will vacuum the remaining ethanol from my oil after all these steps are complete, ending up with zero parts per million solvent (or as close as I can get).
There are many ways to skin this cannabis cat!