My nose during the cold hurts even when im inside my house and my feet/hands/ part of upper arm are extremely colder than the rest of my body

Your nose might: ..hurt inside your house, not because of the cold, but because of the low humidity. Saline nasal spray during the day and application of Vaseline at night might help. The coldness of your feet, hands and arm could indicate problems with your circulation, anemia or a peripheral neuropathy. You should ask your doctor about this. Best wishes. Dr. Anne