Frosty is the title character of the beloved Christmas song "Frosty the Snowman", and a featured character in multiple Christmas stories, most notably a DreamWorks and Rankin/Bass's 1969 film and few of Rankin/Bass specials.
Like in the original song, Frosty portrays as a fun-loving, jolly snowman TBD
The Rankin/Bass version
DreamWorks and Rankin/Bass 1969 film
At the beginning of the original 1969 animated film, Frosty is built by Karen and her friends right after school has closed for Christmas vacation. The wind blows the hat of Professor Hinkle onto Frosty's head, and suddenly the snowman comes to life, saying his cheerful catch phrase, "Happy birthday!" Frosty is good-natured and playful, but also somewhat naive due to his relative youth (having just been "born"). He is unable to count above five and is the world's fastest belly-whopper.
Frosty has two physical weaknesses: the tendency to melt in warm weather, and the hat, without which he becomes another inanimate snowman. (However, when Frosty gets startled by the Traffic Cop and later by the ticket man, his hat briefly jumps off of his head. Also, in Frosty's Winter Wonderland, he is shown lifting his hat off of his head twice.) Karen and her friends offer to help Frosty get to the one place where he could never melt - the North Pole. However, Professor Hinkle chases after Frosty and Karen, trying to steal his hat back, and eventually traps them in a greenhouse full of Christmas poinsettias when Frosty takes Karen inside to warm up due to how cold she had gotten. Fortunately, Santa Claus manages to revive the melted Frosty by letting in a December wind and afterwards takes him to the North Pole.
Rankin/Bass TV specials
Frosty promised to be back again someday, and in Frosty's Winter Wonderland, he fulfills his promise. The character's design is only slightly altered from his original appearance, primarily the addition of a scarf. As much as he enjoys playing with the kids, Frosty becomes lonely when they have to return to their homes. To remedy this, the kids construct a snow-woman, who Frosty names Crystal. She comes to life when Frosty presents her with a bouquet of flowers, a gift of love. Despite the interference of Jack Frost, who attempts to steal Frosty's hat out of jealousy, the couple are wed by a snow parson (and Jack is mollified when asked to serve as best man).
Frosty later appeared in stop-motion animation in the movie Rudolph and Frosty's Christmas in July. By now, he and Crystal have two snow children, Chilly and Milly (the means by which snow people procreate is ignored; possibly, they simply built their own children out of snow). In this production, Frosty is best friends with Rudolph, who serves as adoptive uncle to the children. Frosty and his family accompany Rudolph to Lilly Loraine's Circus by the Sea in Florida, protected by magic amulets provided by the evil Winterbolt, so they can help Rudolph's friend, Milton the Ice Cream Man, with saving his girlfriend's mother's circus from foreclosure.
The pair generally enjoy their time performing with the circus, in spite of Frosty's worries that they may not make it back to the North Pole by the time the amulets wear off. But when Rudolph is tricked by Scratcher into giving the circus's money to Sam Spangles and his nose's light goes out as a result, Frosty comes to his friend's aide, offering to sacrifice his life in exchange for helping Rudolph and protecting his family by giving up his magic hat to Winterbolt. The evil wizard betrays him, but Rudolph is able to retrieve the hat, along with the circus money. To celebrate, Frosty and Rudolph sing a variation of "We're a Couple of Misfits" (from the original Rudolph the Red-Nosed Reindeer special). Frosty and his family eventually do melt after Winterbolt is destroyed, but they are brought back to life by Jack Frost, and they return to the North Pole with Santa.
Frosty the Snowman 2
Appearances in other Christmas media
The Legend of Frosty the Snowman features Bill Fagerbakke as the voice the Rankin/Bass version of Frosty. (Coincidentally, Bill Fagerbakke had previously voiced a parody of Frosty, played by Patrick Star, in the Merry Nickmas short "Patrick the Snowman".)
Appearance in other DreamWorks productions
During the 2014 re-release of Shrek (2001), Frosty, Karen, Hocus Pocus, and the kids made a cameo as one of the exiled fairy tale creatures.
In the theme parks, including DreamWork-themed parks, the costumed characters like Frosty, Karen, Hocus and Majesty Meow can be seen solely during the Christmas events.