Your baby's hand is very cold because you may be open the fan when the weather is very cold or you give the baby some cold drink to eat so the baby is very is very cold. Also you baby always have 手汗because your baby touch some thing very hard so the baby always have 手汗. I think your baby do not need to see the doctor because I Always have a little bit of 手汗 and I do not go to see the doctor.