Ice can get as cold as its environment. For example, in a freezer with an ambient temperature of minus 40 degrees F, ice will continue cooling beyond the freezing point until it, too is minus 40 degrees F.
Theoretically, the only lower limit to the temperature of ice is "absolute zero." Absolute zero is zero degrees on the Kelvin scale and is equal to minus 273 C or minus 469 F. At absolute zero, atoms are unable to move and cease to generate heat. The upper limit to the temperature of ice is the freezing point, which is 32 F and zero C. At this point, water changes from a liquid to a solid and becomes ice.