The Wikipedia article on Jack Frost is very disappointing.
Jack Frost is not really a character from folklore or mythology. He’s really more a turn of phrase. Many sources connect him to a Norse deity named Jokul Frosti, but careful research will reveal a dead end. Namely, Jokul Frosti does not exist. Jokul (Icicle) and Frosti (Frost) are sons – or different names for the same son – of Norse wind god Kari. However, they have no clear connection whatsoever to Jack Frost.
He comes from a long history of personifying the seasons. Frequently someone might refer to Winter or Frost as if they were a person, as Hannah Flagg Gould’s did in her poem “The Frost.” Jack is just a generic man’s name (as in jack of all trades). It's hard to find characters like this from any other season, but in winter there's a wealth of them - Old Man Winter, Snow Queens, Ice Maidens, Mother Holle, etc., etc. There's just something about cold weather that invites this kind of personification.
So here's my timeline on mentions of Jack Frost. Not complete by any means; I'll have to see what I can add to it as I do more research.
1740: In Round about our Coal-Fire: or, Christmas Entertainments:
“This time of Year being cold and frosty generally speaking, or when Jack-Frost commonly takes us by the Nose, the Diversions are within Doors, either in Exercise or by the Fire-side.”
So there's the ancestor of "nipping at your nose," this early already.
7 December 1765: Jack Frost, “To the Author of The Summer’s Tale” St. James’s Chronicle (10 December 1765). (This is just a silly letter to the editor from an anonymous pen, signed Jack Frost.)
5 January 1785: Freeman’s Journal; or, the North-American Intelligencer (Philadelphia) publishes a poem: The Life and Adventures of Jack Frost And his wholesome Advice to all honest hearts at this nipping season. A NEW-YEAR’S SONG. More on this.
1826: Sporting Magazine. “Jack Frost, however, put a veto on our morning’s sport.” The Oxford English Dictionary dates the name Jack Frost to this article, but as we’ve seen, it’s actually older.
1858: Copyright for a book, Jack Frost and Betty Snow; with other tales for wintry nights and rainy days, by John F. Chanter et al. Here Jack Frost and his wife Betty Snow are capricious spirits who freeze everything and kill people.
1861: Jack Frost appears as a fearsome bearded general, bristling with icicles, in a cartoon by Thomas Nast, in Harper’s Weekly. Captioned “Our New Major-General.” It refers to a speech by Major-General Benjamin F. Butler, where he calls “General Jack Frost” “our faithful old Ally of the North.”
1864: The same cartoonist draws Jack Frost again, in an item labeled Central Park Winter.
1872: Hardwick, Traditions, Superstitions and Folk-lore, mentions “The blustering of old Boreas, and the frigid embrace of ‘Jack Frost’.”
1875: Charles Sangster, "Little Jack Frost“. The Jack Frost of this poem has a lot in common with the Jack Frost of Rise of the Guardians - a “nose-biting, prank-playing” creature “capering wildly through storm and sleet,” who is finally ousted by Mother Nature.
1889: In Bates’ poem “Goody Santa Claus,” Jack Frost is the neighbor of the Clauses. (The same poem mentions an Artist of the Autumn Leaves, who might or might not be the same person.)
Now Jack Frost is being associated with Christmas, and that's only going to continue.
1902: Jack Frost features in The Life and Adventures of Santa Claus by L. Frank Baum. (You see what I mean?)
1905: Jack Frost Christmas Stories, by Alix (Alice Brooks). Baltimore.
1909: He’s a character in a skit titled, “An Autumn Carnival.”
1915: Another autumn-themed skit, in Kindergarten Primary Magazine volume 27, mentions Jack. This one also personifies all the months of the year.
1934: Jack Frost, a cartoon short by Ub Iwerks. Jack appears as a weird but friendly little gnome armed with a paintbrush and palette. The villain of the piece is a blue, icicle-bearded Old Man Winter.
1936: Maxfield Parrish, Jack Frost - a picture of a small man (self-portrait) surrounded by painting implements and colorful fall leaves. This was a magazine cover for Collier’s.
1945: “Chestnuts roasting on an open fire, Jack Frost nipping at your nose…” If you live in America, you probably have heard this song at least five billion times in your life.
This website is based on my research into folklore.