'coldest realization' is a realization that is a mixture of shock and perhaps dread/fear knowing something bad is about to happen. When you are in shock or a sudden fear, there is a body response of feeling cold because blood flow shifts from your extremities/face to your body core. This is a natural response to fear or shock. You can feel cold and even shake. The 'coldest realization' draws a comparison to this. The comparison may be metaphorical or literal. In either case, it is saying the shock is sudden and deep.

"The coldest realization" is trying to say "the harshest discovery"... cold is intended to convey a notion of shock and disbelief