Same here, it should not affect your phone (unless by “rather cold” you mean below freezing temperatures…). After all it isn’t supposed to do much during the night (some synchronization, some housekeeping).
Yes, yes, 5G is still the big scary bogeyman, it uses secret Microsoft nanotechnology to induce Covid so the lizard men infiltrating the government can brain-control you! 
Seriously, I’ve been using 5G since I bought my FP4 in 22, and it doesn’t make any difference in battery consumption, at least not in France (where 5G has excellent coverage) and apparently not in Germany either (where 5G coverage is more irregular). People experiencing issues with 5G most likely have their providers to blame.
Yes, I have noticed too that some apps don’t respect that setting. Seems it is more like a proposal than an iron rule. 
As about battery issues: It’s a topic which does reappear regularly, and especially after every OS update. After the A13 update in 2023 there was for instance an issue with some (apparently random) app draining battery (there was a thread about it); For me that app was Quickstep (the launcher), and the problem sort of solved itself after half a year (or I got used to it).
If you make a forum search for “battery drain fp4” a lot of other cases will emerge. Bugs aside, it seems every update further degrades battery capacity. Now is this due to the increasing fragmentation of the OS code (as opposed to a clean install on a brand new FP4), or is it the aging battery which isn’t as forgiving as it was in its youth? Hard to tell.
Some have suggested to factory reset the phone and reinstall everything from scratch to fix that OS fragmentation, something which seems to have worked for some, but not at all for others… So, personally I’d rather suggest to sacrifice a black rooster at midnight on new moon (that would be January 18th): It might not be any more efficient than a system reset, but roasted chicken is tasty so I tend to always prefer that solution… 