Any time a noble or royal lady has a title that is winter themed.
Say you're a queen or a princess, and you find that the Ermine Cape Effect isn't giving you enough of an aura of majesty. You want to seem mysterious, exotic, perhaps even a bit dangerous.
Well, unless you live near the equator, the solution is simple. Choose a word closely related to winter. "Snow" and "Ice" are the most common, but others will do, as long as it evokes the feeling of the cold north. Then make one of your titles "The (winter word) Queen" or "The (winter word) Princess". It doesn't matter what your actual rank or title is. Just use that format.
Then make sure your wardrobe consists of mostly shades of blue, silver, blueish purple, and especially white (but not pink, even if Princesses Prefer Pink). A Pimped-Out Dress and Pimped Out Cape are obvious choices, but you could also have a Happy Holidays Dress, a Sexy Santa Dress, or even a Fur Bikini. Fur trim (white or gray), sapphires, diamonds, and/or silver on your dresses also adds a wintry touch. An Ice Palace wouldn't hurt.
Now watch how everyone speaks of you, with this title. You're now even more incredible in their eyes. You're like some kind of spirit or goddess to them, even if this won't actually give an indication of your personality. You can be good, evil or anything in between. You also could either have super powers (especially using Silver) or just be a Muggle. They won't really know, and that's just the way you want it.
This is also why in holiday festivals and pageants, the winner is usually given this kind of title rather than one that is related to Christmas or any other holiday. These titles are muchcooler.
Note that kings and princes can do this, but it's rare. Mere nobility doing this is rarer still.
Despite the name, Defrosting Ice Queen isn't related to this, as that's about personality, and this is about titles, although it often applies to sympathetic Winter Ladies.
Compare Ice Queen, An Ice Person, Evil Is Deathly Cold, An Ice Suit.
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In the Sailor Moon S movie, the villain is Princess Snow Kaguya. She appears to be actually MADE of ice.
The Ice Princess from The Adventures of Sharkboy and Lavagirl... although she genuinely possesses the title, as her father - the Ice King - is a gigantic humanoid composed entirely of ice, and he really is King of an ice kingdom.
The Winter Queen by Jane Stevenson is a novel about the actual Queen of Bohemia and her (fictional) husband-in-exile who is also an ex-African prince, slave, and theology student.
Queen Selenay of the Heralds of Valdemar series wears white exclusively — but this is justified since she, like all Heralds, wears white on duty. In one story set during her early days on the throne, she commissions a Winter Festival to distract her from her mourning for her father.
Mercedes Lackey also has two examples from her Elemental Masters and Tales of the Five Hundred Kingdoms series. Both are based on The Snow Queen, and the characters are Cordelia and unsurprisingly, The Snow Queen. (In the latter book there are actually two Snow Queens — one a Fairy Godmother playing the part and the other a straight example).
In The Dresden Files, the Winter Court make this pretty much literal. Winter Lady Maeve, Winter Queen Mab, and Mother Winter are pretty much the embodiment of cold.
For a rare male version of the trope, in the backstory to A Song of Ice and Fire, the Kings in the North (ruling from the castle of Winterfell) used to be colloquially known as the Kings of Winter, fitting the recurring ice/winter motif of House Stark. Teenage king Robb Stark revives this title when he is raised up to King in the North, King of the Trident, and King of Winter when he rebels against the Iron Throne. Presumably any woman to inherit the Northern crown would be the Queen of Winter.
The titular villainess from Caverns of the Snow Witch in the Fighting Fantasy series. Other books set in this universe have also referenced the character.
Live Action TV
Tin Man plays with this trope by having the party's first real lead on the Queen (and DG's identity) being in an ice-encased palace.
In Hawaiian Mythology, Poli'ahu, and her sisters Lilinoe, Kahoupokane, and Waia'u.
In the Warhammer Fantasy world, the northern human country of Kislev is ruled by Tzarina Katarin, also known as the Ice Queen or Ice Empress. She even uses a special ice-themed magic lore to which no other currently released character has access.
The roleplaying game makes it clear that there is an entire group of Ice Witches who can use that Lore, and Tzarinas have to be at least competent with it. This doesn't apply to Tzars since only women can use ice magic.
Jezra Wagner, the "Ice Queen", is a spectre that haunts the mountains of Barovia in the Ravenloft setting. Not royal, but a noblewoman in life; her ice-pale looks and flesh-freezing touch certainly fit this trope.
Also, the Winter Court is an actual group of changelings who represent (and feed off) sorrow. Yes, their female rulers are called Queens. (Though the book notes that many Snowskins don't join the Winter Court because they want to avoid becoming this trope.)
The Ghost of Christmas Past in A Contemporary Theatre's more recent productions of A Christmas Carol.
RWBY has a wealthy heiress who is literally named Weiss Schneenote German for 'Snow White' and dresses mostly in shades of blue and white, the former matching her hair. Her family's logo is also an intricate snowflake, in case you didn't get that she's winter-themed.
The Rankin/Bass special Rudolph and Frosty's Christmas in July gives an alternate backstory for the glowing nose of the titular Rudolph, explaining that it was a power bestowed on him in infancy by the Lady Boreal, a Winter Royal Lady who is sort of a personification of the Northern Lights.
Princess Yue of the Northern Water Tribe in Avatar: The Last Airbender . It's downplayed in that while she fills a lot of aspects of the trope, it's treated as basically coincidental and she's relatively normal for a princess. Mostly.