Banana Joe is correct. The question is well placed, however.
Let's say for -10 degrees you'd be flying inside the temp envelope for the procedure, designer's work protects you from the obstacles. But your on-board altimeter mis-indicates due to cold temperature error (ISA-25). So home come do not need to increase the minima (moreover, the correct wording is
must not increase)? After all, Doc 8168 tells you to compensate for that and the geometry is rather clear - don't correct = get below. Hm?
Nice catch.
Short review: the Operator minima altitude is the operators' add-on PLUS [the higher of (obstacle elevation + minimum obstacle clearance);(system minima)]
A) Hence in a case where the minima are restricted by the obstacle, the OCA = ELEV + MOC is calculated by the designer with non-compensated baro already accounted for down to the low temp limit.
B) If there are no /low obstacles and the lowest system minima (arbitrary number) defines the value, there are no obstacles to hit by definition.
Wait, the "b" above would work, but in aviation is just plain wrong just by the sound of it. Being clear of the terrain does not make it right. Plus, how do you justify being lower than the minima as that's where the altimeter will take you?
Answer: Lesser of two evils.
If you would compensate the minima while flying a not-compensated profile as authorised by the temperature envelope, you'd effectively move the point of reaching that minima further from the runway. This will invalidate the RVR / VIS calculation and might have detrimental effects on the safety level end economy.
Then: As you are always safe from obstacles by the full prescribed margin with altimeter error already accounted for (OCA by procedure design in case A), it is accepted to have MDA geometrically lower then system minima (case B) for the sake of retaining RVR/VIS values and increasing the likelyhood of obtaining sufficient visual reference.
Capt Scribble Many operators require correcting the MisAp alt, without seeing that by definition is not a minimum altitude but a maximum "climb-to" altitude.