Cold temp corrections on LNAV appr

[EMIT]

In the subsequent postings, there is some disagreement as to whether the approach altitude of 3.000 ft should be corrected for low temperature or not. Some posters are emphatic that all (minimum) altitudes should be increased, others state that altitudes should be increased, when necessary. So what is true?
Let’s have a look at the (European) law (quotes from Regulation (EU) 965/2012 on air operations ).

CAT.OP.MPA.125 Instrument departure and approach procedures
(a) The operator shall ensure that instrument departure and approach procedures established by the State of the aerodrome are used.
(b) Notwithstanding (a), the commander may accept an ATC clearance to deviate from a published departure or arrival route, provided obstacle clearance criteria are observed and full account is taken of the operating conditions. In any case, the final approach shall be flown visually or in accordance with the established instrument approach procedures.
(c) Notwithstanding (a), the operator may use procedures other than those referred to in (a) provided they have been approved by the State in which the aerodrome is located and are specified in the operations manual.

AMC2 CAT.OP.MPA.126 Performance-based navigation
…
(2) Temperature compensation

(i) For RNP APCH operations to LNAV/VNAV minima using Baro VNAV:
(A) the flight crew should not commence the approach when the aerodrome temperature is outside the promulgated aerodrome temperature limits for the procedure unless the area navigation system is equipped with approved temperature compensation for the final approach;
(B) when the temperature is within promulgated limits, the flight crew should not make compensation to the altitude at the FAF and DA/H;
(C) since only the final approach segment is protected by the promulgated aerodrome temperature limits, the flight crew should consider the effect of temperature on terrain and obstacle clearance in other phases of flight.

(ii) For RNP APCH operations to LNAV minima, the flight crew should consider the effect of temperature on terrain and obstacle clearance in all phases of flight, in particular on any step-down fix.

Another relevant document is ICAO Doc 8168, Aircraft Operations (relevant, but not the law).
From there. The relevant paragraph.

4.3 TEMPERATURE CORRECTION
4.3.1 Requirement for temperature correction
The calculated minimum safe altitudes/heights must be adjusted when the ambient temperature on the surface is much lower than that predicted by the standard atmosphere. In such conditions, an approximate correction is 4 per cent height increase for every 10°C below standard temperature as measured at the altimeter setting source. This is safe for all altimeter setting source altitudes for temperatures above –15°C.
4.3.2 Tabulated corrections
For colder temperatures, a more accurate correction should be obtained from Tables III-1-4-1 a) and III-1-4-1 b). These tables are calculated for a sea level aerodrome. They are therefore conservative when applied at higher aerodromes.