The tradition thinks of warmth as something made in the middle and sent outward, and it is not surprised that the hands and feet, the furthest points from the middle, are where a shortfall is felt first. The question a Chinese physician asks is not why the hands are cold but why the warmth is not arriving, and there are three usual answers: there is not enough of it, there is not enough carrying it, or something is holding it back.
The three feel different. The person short of yang is cold all over, hands and feet worst, and loves the sun, the bath and the warm drink. The person short of qi and blood has pale, cold ends, gets dizzy standing up and tired on the stairs. The person whose qi is bound has icy hands on a body that is perfectly warm, worse on a stressful day, and finds they thaw the moment they go for a walk. The tongue tells them apart in a minute.