My 5 month old sons' hand and feet are ice cold and kinda bluish. He has always had cold feet but his hands have never been this cold.?

Normal finding. Babies most important job is to grow bigger so they are designed to avoid energy loss(heat) by shifting circulation away from the top of their skin of fingers, toes&ears to deeper skin.Stick the same bluish toes in warm water & they pink up.A better gage of oxygen flow is to open & look at the inside of the eyelid. Keep baby in a onezie with footies& this won't bother you or baby.
Capillary Refill. You can also check your son's capillary refill under his fingernails and toenails. Briefly, and gently, depress a nail until the skin underneath blanches, then let go and see how quickly the blood returns to it. It should almost instantly revert back after blanching. If there is a delay in any of the fingers/toes, see your child's doctor. If brisk, then he's fine but ok to cover hands.