Christmas hat

Christmas hats were what the Twelfth Doctor called the coloured paper crown-shaped "hat" which people wore at Christmas. Having seen people used them, he observed that one "put them on and absolutely anything seem[ed] funny". (TV: Last Christmas) They came from Christmas crackers. (TV: The Christmas Invasion)

History
While celebrating Christmas Day at 48 Bucknall House in 2006, the Tenth Doctor wore a red Christmas hat while Rose Tyler won a hat from a cracker which she pulled with the Doctor. Finding that the hat was pink, Rose commented to her mother that it would suit her more. Immediately after, the Doctor and Rose's attention was turned to a BBC News 24 broadcast featuring Harriet Jones. Following this, the pair removed their hats as they went outside to observe the snow, actually ash from the destroyed Sycorax ship. (TV: The Christmas Invasion)

In Donna's World, Donna Noble celebrated Christmas at a bar with her colleagues. Donna wore a gold Christmas hat, as did Veena Brady, while Alice Coltrane wore a yellow hat. (TV: Turn Left)

On a Christmas during the 2010s, Clara Oswald wore a green Christmas hat while cooking Christmas dinner for her family. Her father, Dave Oswald, wore a purple hat, while her grandmother wore a gold one. (TV: The Time of the Doctor)

In a shared dream induced by the dream crabs in which they celebrated Christmas at the latter's house, the Twelfth Doctor provided Christmas hats, with Clara Oswald suggesting that he would be the exception to the rule that the hats made everything funny. The Doctor wore a purple Christmas hat while putting a yellow one on Clara's head. (TV: Last Christmas)

Celebrating Christmas in the latter's office at St Luke's University in 2016, Bill Potts wore a red Christmas hat while the Doctor wore a blue one. (TV: The Pilot)