is frosty the snowman public domain

Yes, "Frosty the Snowman" is indeed in the public domain. The song and characters were originally created by Steve Nelson and Jack Rollins in 1950, but the copyright on their work has expired, which means it is now in the public domain and can be used freely by anyone without needing permission or paying royalties. This means that you are free to use the song and characters in any way you wish, including creating your own works or derivative works based on them. However, it's always important to respect the original creators and their intellectual property, even when using public domain works.