Is it normal if an infant is running a high temp for their hands n feet to turn ice cold for the duration of the fever? and why

NO not normal: An infant running a "high temp" should be seen to determine the etiology. I would recommend calling your health care provider and reporting this.

No: Assuming that the infant's hands and feet are not exposed to cold air, bring the infant to a Dr! If the hands and feet are turning ice cold it could be due to a drop in blood pressure or worsening infection and it is not safe to ignore this. Of course if the child is smiling and acting normal it may be serious, but a high temp and cold extremities is worrisome. Please have the infant seen ASAP.