Cotton, aka "Death Cloth" is not something you want to wear outside in winter or any season with the exception of hottest Summer. Other fabrics are safer like wool or synthetic.
Cotton is dangerous because of its hydro-philic (water loving) nature.
Wet cotton stays wet and dries slowly. If you have wet cotton on your skin and it is cold outside, you will lose heat through evaporation and in winter this can be dangerous.
So leave the cotton at home and wear wool or synthetics out there.
If you want to save some money on some warm layers I highly recommend thrift stores - wool pants and thin wool sweaters are treasures to be hunted for. If you cannot find the wool (first choice) you will definitely be able to locate some polyester. Thrift stores are shrines to polyester.