The lower temperature limit for airframe icing is based on the low concentration of supercooled liquid droplets in the atmosphere at low temperatures. Below a SAT of -40 degC, there's not enough water there in the liquid phase to cause (significant) icing. The temperature of the aircraft skin doesn't affect that concentration, and the limit is therefore an SAT.
(I'm surprised you saw ice at -40 degC. Is that a regular occurence?)
The upper limit is based on the highest temperature at which some part of the airframe is below zero. Because it's about skin temperature, the TAT is what's important. In aircraft with high wing-loading in low static pressure, this can happen at TATs up to +10 degC, because the part of the upper surface where most of the lift comes from is at lower pressure, and therefore lower temperature than the stagnation points.