Help me find this recorded version of "Frosty the Snowman"

A while ago, I’d occasionally hear a certain recording of “Frosty the Snowman” on the radio. It had someone (maybe several people?) singing it - I think it may have been someone fairly well-known, but I don’t remember. What I remember about the song was that throughout the song, there was a little counter-melody played in unison (well, same tune, many octaves apart) by a piccolo and a bass clarinet at the same time.

I realize that this isn’t much to go on, but can anyone help me find this?

Thanks.

This it?
Burl Ives - Frosty The Snowman

This probably isn’t it but in searching I found this amazing home made video of some teenagers lip-syncing to Harry Connick Jr’s version.

And by amazing, I mean super terrible.

Here’s a place that has a lot of different samples:

http://singwenowell.com/songdetail.aspx?songSelected=17

Hmm, that might be it, although that’s a bassoon rather than a bass clarinet. Maybe I was remembering wrong? Or else, there exists a version with a bass clarinet out there somewhere.