If there's one thing that a mother, especially of a young child, should not leave the house without is a scarf. Why, you ask! Because it is the single most handy object that will rescue you in many situations. If you want to know what situations I am referring to, read on.
Blanket for the baby: Babies always fall asleep in the car, and it is better you cover them so they are cozy and sleep longer. You can use a scarf in a pinch and don't have to worry about keeping an extra blanket in the car.
Cover for stroller/ carseat: You do get the fancy stroller covers that help keep the sunlight out, but why add one more thing to carry in your already bulky diaper bag? A scarf does the job perfectly well.
Nursing cover: The nursing covers available in market look more like an apron, and are seldom made of soft, airy fabric. Not that there is anything wrong with nursing in public, but if you do get a little conscious, you can always use a scarf to cover yourself.
Cover spill-ups/ stains: As a new mother, you will soon get used to spill-ups and stains on your shirt. If not your baby, then your leaking boobs will do the job. A scarf will definitely come in handy to cover the stain.