In the USA (and most developed countries) the QNH given for a station is corrected for local station temperature.
It's not a question of correcting the airport QNH for local temperature. It's about the temperature of the column of air between airport level and DH.
In indicating the altitude at DH, the altimeter assumes that a pressure difference of (say) 7 mbar is equal to 200 ft. With a temperature 30 degC below ISA (i.e. -15 degC), the same pressure difference occurs in 10% less height. So the altimeter overreads by 20 ft.
For typical precision approach DHs, it's hardly worth making a correction. But for an MDH of 1000 ft on a non-precision approach, it would eat 100 ft off your terrain clearance if you didn't make a correction for temperature.