There isn't a specific fairy tale for Jack Frost, just some traditional poems, (though there are a few picture books) but he's a character that pops up a lot in Winter fairy and folktales in various guises - and he's often a different character from The Winter King.
Traditionally, Jack Frost (or King Frost or Father Frost), is an elf-like creature or sprite and ranges from elf-size-small to human size to the size of the wind, depending on what mischief he's up to. He's credited with decorating window panes and frozen surfaces with (spiked and frosty or 'fern-like') ice patterns, sometimes with his breath, sometimes with "his silver brush". He's also fond of nipping at fingers, toes and noses.
Jack Frostby Oliver Herford
I particularly like Frank L. Baum's treatment of the character in which Jack Frost is actually the son of The Winter King (or Frost King) and, like most Jack characters, employs a strong streak of mischief in all he does. Santa Claus actually likes him (calls him "a jolly rogue") but doesn't particularly trust him and asks specifically that Jack spare the children. Jack sobers enough to reply he will if he can.
Jack Frostby Eric Kincaid
Another activity attributed to Jack in literature includes the ability to freeze shadows, separating them from their owners and giving them their own autonomy (that appears to have originated from Baum too).
He's also been represented as having the ability to project ice and cold, be prone to jealousy, turn from mischievous to downright nasty (including amassing leagues of Goblins to help him take over Fairyland) or to simply be the light-hearted herald (sometimes filling a court jester role) of the Winter King.
Jack Frostby Arthur Rackham
A composite of the Jack Frost covers from the "Fables" seriescreated by Bill Willingham
This character has appeared in countless myth-based novels and stories since in all shapes and forms, playing the protagonist to the villain. The Fables series also uses the character of Jack Frost too with his story and legend continuing to grow in various installments. He's such a versatile character, with many facets from country to country (a tiny pixie through to Norse heavy-weight frost-giant - with frost-giant brothers), I'm actually surprised we haven't seen more of this fellow*.
*Wikipedia has a growing list of references in literature and film and, though it's still far from complete, it's a good place to start researching (see HERE).
