I read the posts regarding the Winter Bash but I still can not figure out what are the functions of these hats? I got one and have not clue of its uses. Please anyone could send me a link that explains how they work? their uses?
They're not 'useful', per se. They just attach to your avatar - they're cosmetic. (They also don't exist on Meta, apparently.) You can choose not to have your avatar 'wear' a hat, and also disable them entirely, in the "your hats" section in your profile on the main site - you can reach it through the snowflake icon in the black bar up top.
The main point is that they look rockin'.