The Winter Bash notifications do not work like in previous years:
Once you get a new hat, you need to refresh the page (or open a new page) to see a change in achieved hats, and then only a blue circle with a number shows (tested on FF and Chrome, both latest versions).
Notifications do not live refresh and also the color of the "snowflake" svg icon is not being changed, when a new hat has arrived. It used to look similar to this:
Note: The live refresh for Notifications for Inbox, Achievements and Reputation appear as supposed.