I would say cone is better over all on a turbo car. Regardless whether the air is cold is irrelevant. If the air is freezing cold once it goes through the red hot turbo it will turn that into hot air. Turning hot air into cold air is the job of the intercooler.
If running higher than standard power I would say a panel filter inside the standard air box is more restrictive than a free flowing cone filter.
Simple way to test this would be to do a vagcom log on your mass airflow with both cone and panel filters
It does matter it's all about the density and mass of the air, colder air is more dense than hot air, google it, just because it goes through a hot turbo yes intercoolers the
lower the charge temp on Intake is important too, and a panel filter is way better than a cone filter, if cone filters were so good why are they not fitted as standard, because they cause heat soak, there is no proof that they increase bhp over a panel filter I have been modding cars for over 25 years and not just on my drive I made it my business most factory airboxs will be capable of upto 400bhp, a cone filter does nothing but sound good and suck hot air from heat soak around the engine bay, if you want the intake to work it has to be either in a sealed box with an intake pipe behind the grill or the filter inside the wheel arch again sealed from water ingress and a cold air ram pipe to feed it cold air,
But this is just my opinion of years and years seeing cars on dynos suffering from cone filters,
If you want an intake that works, uses hard pipe from the turbo to a sealed cone filer in the inner wheel arch then a cold air ram pipe to feed that, no water ingress and deffo no heat soak,