Eerie song about Frosty

Since I was little, I always have these kind of funny- sad feeling about this song, imagine- at first it was a happy joyful song, read this for sure:

Frosty the Snowman
Is a fairytale they say
He was made of snow
But the children know
How he came to life one day

There must have been some magic
In that old silk hat they found
For when they placed it on his head
He began to dance around

Frosty the Snowman
Was alive as he could be
And the children say
He could laugh and play
Just the same as you and me

and sudddenly.....the worst part is to be come....


Frosty the Snowman
Knew the sun was hot that day
So he said let's run
And we'll have some fun
Now before I melt away

Meltt...? Howcome? Mooom.. why he has to melt, make him stay, pleaase..- I don't want this part, make the song go faster.. argghhh...