Blue hands and feet

My daughter was born on the 25th of october, and I was going through pictures of when she was born, her feet and hands were really purple /blue, i saw it when I first held her but figured it was because she was just born so it didn't bother me, color is normal now, but she's cold all the time her feet and hands they are so cold to the touch, and my room is super hot and cozy even to the point where I start to sweat, but she seems to be cold she'll have hiccups, she's always covered and has mittens and socks and a blanket, i asked her pediatrician she said to put her on my skin under a blanket to regulate her temperature but it hasn't helped, is this what all babies go through? She was also born with the umbilical super short according to Dr it was half of the normal sized one, just don't know what else to do to make my baby comfortable.