bunnyip,
Indicated altitude above the airport is not the problem. Altimeters that are used to determine QNH are calibrated at ISA. Temperatures colder than ISA cause inherent errors.
Non-precision approaches are also not the only problem. An ILS to minimums would actually take you closer to the landing threshold and you're true altitude at DH would be lower than published if corrections for low temperature are not made.
ATC in the US will assign altitudes that are based on ISA temperatures. It is up to you to make the corrections so that your indicated altitude and true altitude are the same.