Despite all the PITCHBLOTs etc. that we were taught as young Bloggses, all altimetry systems have only 3 basic errors:
1. They're not perfect machines.
2. They're installed in a moving aircraft rather than being free-standing in space.
3. They are only calibrated for International Standard Atmospheric conditions and have no idea of the actual values of lapse rate prevailing directly at and below their position.
You can reduce mechanical imperfections with, for example, an electronic display. You can also reduce installation errors by using a clever Air Data Unit or Central Air Data Computer. The OAT feed merely assists in reducing the errors in the 'physics' of the aircraft installation. However, unless you point-plot the actual environmental lapse rate in the atmosphere in which you are flying - which is obviously totally impossible - you cannot, Hophorrigan, correct AUTOMATICALLY for non-ISA atmospheres. This doesn't matter when everyone is flying on 1013 (or 29.92 for those still using quaint old inches) because everyone will have the same error due to non-ISA atmospheric conditions. But, near the ground in cold temperatures it is absolutely essential that temperatur error correction is applied to ALL altimeters. If that means your indicated altitude will differ from a published STAR altitude in order to achieve safe separation between metal and stone, ADVISE ATC - they won't mind!!
Incidentally, the meat bombs who made such a tragically nasty pink stain jumping out over the South Pole probably learned rather too late about temperature error correction IMHO - they were much lower than their altimeters said when they pulled their ripcords!! Hophorrigan - listen to those in this thread who are trying to protect you and your passengers from an unexpected close encounter of the worst kind with terra firma!!