What was the name of the little girl in Frosty the Snowman?
The snowman's name was Frosty. Hence the name, "Frosty the Snowman." If this is not the answer you were expecting, then you may be asking about "the Bumble", the abominable snowman character from Rudolph the Red Nose Reindeer. Or, you may be asking about the narrator snowman, who was either Burl Ives or Jimmy Durante, depending upon which show you're asking about.
The word 'frosty' is an adjective (frosty, frostier, frostiest), a word that describes a noun as very cold with frost forming on surfaces; covered with frost. The noun form for the adjective frosty is frostiness. The form, Frosty, is a proper noun, the name of a character in a children's song and stories, Frosty the Snowman.