You can see a partial list of sites where you've earned the hat in your hat rack. Your screen shot does not show this site there, though in theory it could be hidden behind "10 other sites". You can see the complete list by opening the hat on the Winterbash site. Click on the hat to see a display like this:
If you do that and find this site in the list please update with a screenshot. I predict that you won't find this site on the list.
You can wear hats that you've earned anywhere on the network; just because you're wearing it here doesn't mean you earned it here.