When I had seriously low ferritin, I felt cold. I could not make my body feel warm even under comforters and even wearing socks. I heated my apartment in NoCal which I never do otherwise. Feeling cold is a common symptom of anemia. Mine went away as ferritin improved. I do not know if this can be connected to periods but maybe as you start losing iron with blood, your body reacts?? not sure it is possible but just a thought.