All minimum altitudes should be corrected for low temp except procedures that are designed down to a certain temp, normally -15 or -20 C. These RNP procedures are not allowed to be flown outside the minimum temperatures.
No, not all ATC units correct for low temp. If they clear you to, say 3000 ft, and this is the MSA, add the required correction and tell them you will maintain this altitude due low temp.
If your FMC autocorrects for low temp, good for you. I have never used one that could do that.