Here is the list of all non-secret hats, some secret hats and their references:
011: 011 was chosen because you get the hat when you get 11 hats. This was named after Eleven on Stranger Things who happens to have a tattoo with '011'. The character also loves waffles, and wears a pink shirt with a blue jacket.
24: For 24 karat gold.
925: Sterling silver is typically stamped with .925.
Abominable: Reference to the Abominable Snowman or the Yeti (mainly Bumble). As the snowman is considered an evil creature who devours people, deleting or closing a question awards this hat.
Bûche de Noël (Yule log cake): It is a dessert served on Christmas. Hence an activity on Christmas day gifts this hat. Buche and Noël means respectively log and Christmas in French.
Egoist: A selfish person (who asks and answers their own posts). The hat depicts a selfie stick.
Hero of Questions: This hat is a reference to the hat worn by Jayne Cobb, a mercenary on the show Firefly. Jayne Cobb is also called the "Hero of Canton", due to some unwitting heroics in one episode, hence the name of the hat.
I Am Your Father: A reference to this Star Wars scene. The name was chosen because Haney felt that it was witty.
I Have A Little Dreidel: a Dreidel is a small spinning top which is played with during the celebration of Hanukkah, a Jewish holiday. The hat's name is taken from the children's song of the same name.
Lifesaver: The hat is the Lifebuoy Ring, Which is used to save people who are drowning. The meaning perhaps is related to Tumbleweeds being questions that are drowning amongst the other posts.
Like Clockwork: a reference to A Clockwork Orange. The hat is worn by the film's protagonist.
Loungin' Around: Since it requires the mobile app, this hat can be obtained without leaving your couch, where you might be said to lounge. One who lounges on a couch is sometimes referred to as a couch potato. The image is accordingly a reference to the Mr. Potato Head toy.
Maverick: Reference to Top Gun character Pete "Maverick" Mitchell, who saves a comrade which is about to crash by heroic action.
Mmmm Bacon: This hat is awarded on what some people claim to be Bacon Day.
No Longer Grinchy: This is in reference to the Dr. Seuss character, the Grinch. The Grinch tries to stop Christmas from coming in a nearby village, Whoville, by stealing all the decorations, presents, and Christmas dinner foods in town on Christmas Eve. When this doesn't work, the Grinch becomes a nicer character. This is the santa hat the Grinch wears, along with the Grinch's mouth smiling. The reopen or undelete requirement is likely in reference to the Grinch growing kinder and paying things back to the people of Whoville.
Polymath: A polymath is an expert in many different subject areas. The hat is a depiction of Leonardo da Vinci. Thus posting on 3 different sites would depict your wide knowledge.
Search You Must: Reference to Yoda, in particular his choice of English grammar
Snaphat: Reference to the Snapchat app.
The Hatter: named after The Hatter from Alice in Wonderland. He is stuck at 6pm forever, and the hat is awarded when you post a question when it's 6pm somewhere in the world (disregarding seconds). Note that there are timezones with a x:30 and x:45 UTC offset which lead to unpredictable calculations.
The NeverEnding Story: a reference to the 1984 fantasy movie The NeverEnding Story. The hat represents Falkor, the friendly "luckdragon" in the movie. The hat is presumably named so because one's achievements as a developer are an ongoing story, so it's a story that "never ends".
What's Up, Doc: Reference to a typical saying by/from Bugs Bunny. Here "Doc" refers to SO's Documentation. The hat depicts Bugs Bunny's ears and the carrot which is always portrayed along with him.
At the end of Winter Bash, the community managers and SE employees (is there a difference?) will create a Meta Stack Exchange explaining the secret hats, how to earn them, and the reason why they were created/named that way.