it's a matter of degrees, meaning the colder it gets the more stuff you add. for what you mention I was very excited to get my cycling specific headband! :-)
I have a
Pearl Izumi Thermal Headband and I love it!
http://www.rei.com/product/837209/pearl-izumi-thermal-headband,-black?preferredSku=8372090001&cm_mmc=cse_PLA-_-pla-_-product-_-8372090001&mr:referralID=f549ec49-2486-11e3-a88a-001b2166becc