Is it normal to be cold intolerance when having periods?

Yes: Your hormones (estrogen & progesterone) are in flux and can also be associated with this sensation. If you have other symptoms like hair loss, weight gain, heavier or irregular periods, this can also be a sign of a thyroid condition. A common condition associated with menstruation is anemia (low blood count). One manifestation of anemia is being cold. I would discuss this with your doctor.