Can't Un-Hear It: Just like Billie Mae Richards' iconic performance as Rudolph the Red-Nosed Reindeer, Jackie Vernon's performance as Frosty the Snowman has become the default voice of the character with the general public. While Frosty has since been voiced by John Goodman in Frosty Returns (not by Rankin/Bass) and Bill Fagerbakke in The Legend of Frosty the Snowman (which uses the Rankin/Bass design and Hinkle making a non-speaking cameo appearance), none of them had become as memorable as Vernon's performance.
Fan Nickname: The children (Karen, Holly, Tommy and Sarah) who help Frosty are known as "snow angels".
First Installment Wins: Much like Rudolph, the original special is the only one that most people would agree is great, but the later installments either don't work or ended up with mixed results.
Jerkass Woobie: Professor Hinkle. He is still a greedy and self-centered jerk to almost everyone around him, even ignoring him melting Frosty by locking him inside a greenhouse. But given the amount of grief he suffers in the special including (though not limited too) failing miserably at his magic acts, being trampled by a classroom full of kids, and losing his magic hat to a talking snowman, it's not hard to feel just a tad bit sorry for him.
Moe: Karen, and how! She's kind and sweet to her friends, and willing to make sure Frosty never melts before it's too late.
Moment of Awesome: So after Santa rebuilt Frosty and was about to put the hat on, Hinkle comes to grab it again. How does Santa put an end to it? By threatening to never give him any more presents for the rest of his life. It instantly shuts him up.
Hinkle crosses this when he locks Frosty inside the greenhouse, allowing him to melt in the process.
Possibly even earlier when he douses Karen's campfire, which was the only thing between her and freezing to death. It's especially bad because he does so for no good reason. Just out of petty spite towards the girl for interfering with him. At least melting Frosty helped Hinkle achieve his goal of getting the hat back, but endangering a little girl's life achieves nothing.
The worst part about Hinkle is, he wants the hat back solely because of greed, claiming he'd be "a billionaire magician" if he had it's very real magic at his side. That's kind of low.
Principal Pankley in Legend of Frostyin addition to orchestrating the obligatory Disney Death of Frosty in the movie, also put Walter in danger by having them skate on thin ice, and expresses a callous disregard about it to Walter.
Sweet Dreams Fuel: The first one in particular, but all of the other specials are this to an extent. They seem tailor made to give that warm and fuzzy feeling.
Tear Dryer: Frosty and Karen gets trapped in a greenhouse by Hinkle. Though Santa comes in time to free them, Frosty has melted, and Karen is crying over his puddle. Then, Santa brings in some Christmas magic, and Frosty is immediately revived, making the ending happy with the power of a Christmas Miracle.
Unfortunate Character Design: The fact that Karen is drawn without pants (or skin-toned pants), as well as adding up an infamous freeze frame where Professor Hinkle is looking at her crotch when she is telling him that his hat isn't his anymore because he threw it away from frustration, makes more modern viewers feel quite uncomfortable with it.
A minor example, but Hocus' motions when mimicking the President of the United States directly mirror that of Richard Nixon, who was in his first year in office at the time the special was produced.
Frosty's comments about how the President of the U.S. and the United States Marines couldn't help get him to the North Pole. These take on a darker meaning when one considers the special was also made during the Vietnam War and at a time many Americans were becoming increasingly tired of the war and aware their side was losing.
Values Dissonance: Anti-smoking groups these days would go nuts over Frosty's corncob pipe, especially considering the children built him with one. Never mind it's never lit (he is made of snow, after all).
by Nothing But Cartoons posits a lot, namely that Professor Hinkle is a Cosmic Plaything undergoing Sanity Slippage, the kids are Frosty-worshiping cultists who practically stole Hinkle's hat, and Frosty is a total Idiot Houdini.