How much the true altitude will be lower than indicated altitude by 10°C colder?
It's not a linear deviation so it depends on the altitude and the temperature at that altitude.  The deviation gets worse as you go higher and colder. 

Lower and warmer, the error for 10 deg is very small, but higher and colder it can be a couple hundred feet. 

Everybody uses a standard table that you can find all over the place with Google.  See here on Page 33 of the General Section of the Canada Air Pilot CAP GEN (IFR approach plates for Canada)  which explains how to apply the corrections, and can also be found in the AIM.  They are only used for IFR use for correcting altitudes for instrument procedures when close to the ground, and are generally not applied unless the temperature at the airport is below freezing.