To me a scarf is the thing you wear around your neck outside, and a dressy scarf is what you wear as a fashion accent.
Mufflers are a car part that wears out like clockwork on Nissan Sentras.
To add to the confusion, before I opened the thread, I was wondering if you might be asking about neck gaiters, which are a tube you wear around your neck and pull up over your nose if it’s super-cold outside. I just finished knitting a few of them. I like them for outdoor tasks, because they keep my face and neck warm, but don’t dangle in my way or come un-tied. My kids like them for keeping warm at the bus stop. Here is a practical example of a gaiter:
http://www.gemplers.com/product/151071/Carhartt-WA012-Womens-Striped-Knit-Neck-Gaiter
I grew up in southeastern Wisconsin, calling a scarf a scarf. I never heard of gaiters till a year or two ago, but I would have loved having them in my Wisconsin childhood.