According to me the cold temperature corrections have to be done for all altitudes passed the FAF and the corrections are in function of the Height and the temperature deviation.
Whe use a table where you enter at one side with the HAT/HAA and with the temperature on the other side. You then get the amount of feet to add to your minima.
Therefore if you have the same temperature deviation, an approach with a higher HAT will require a bigger correction.
As for the set of corrections, it is merely a correction because the altimeter assumes ISA temperature lapse, where cold temperatures would give a deviation in the unsafe direction (indicating higher than you really are). This error should be the same in all parts of the world.
Bart