Answer:
This is a pretty open ended question but Imma do the best I can.
When your core temperature is cold enough, the heart has to work extra hard to pump blood to your extremities. so it cuts off blood flow to your fingers and toes, then legs and arms. Your heart is working its hardest to circulate blood to only the vital organs to keep them from dying. If you endure hypothermic temperatures for too long your fingers and limbs can essentially die from not having blood flow to them.