Unfortunately, no. The hats are not permanent. Winter Bash hats are always temporary that get put back in the box when hat season is over.
If you want hats to remain, then you should wear a hat, take a screenshot of your avatar with it and change your avatar as you'd like. But we've got no plans to make hats permanent.
Last year's poll was so clearly in favour of Hats (see Should GIS participate in the 2014 “Winter Bash”?) that I proposed to the other mods that we simply accept the default option which is that we get Hats.
Just for a bit more transparency, the relevant contents of the email to moderators about this year's hats were:
As moderators in our network, you ...
As GIS users, perhaps we are aware that it's only winter north of the Tropic of Cancer, which is much less than half of the world.
Perhaps the name 'winter bash' is poorly chosen.
(And who likes hats anyway)
YES, GIS should participate in the 2014 “Winter Bash”.
The reasons are :
There is a personal right for every person not to join it by choosing "I hate hats" option.
There is no option for those who want to use that nice hat if GIS does not participate in the "Winter Bash".
see: Winter Bash 2012 and 2013