Some simple crochet patterns for winter scarves include the 2 1/2-hour-or-less scarf and the aqua blue scarf. As of 2015, both of these patterns are available online for free.
The 2 1/2-hour-or-less scarf pattern makes a scarf that's long enough to wrap around the neck with plenty of additional crochet to make a knot or tie it in a unique way. The pattern is a PDF, so the knitter can download it to a computer or print it easily.
The aqua blue scarf is a longer scarf that ties with ends hanging down the chest. It features a textured design that shows skill and feels nice to the touch. Knitters can print the PDF file or download it for later use.