Why does cold weather feel colder inside?

One reason is that when you have been out in the cold, your hands feet and exposed features of your face will take time to recover as the blood circulation improves and supplied warm blood to capillaries. So the relatively warm room you enter will not immediately feel warm until the blood has regained its normal circulation. Other factors are that windows are cooled from the outside and condensation forms on the inside because of moisture in the air. For this condensation to evaporate requires heat, which will be extracted from the room and the air near the windows will be cooled. The cold air will descend and form a draught at floor level and this will tend to make the room cooler.