Old Duet

[Ginny Gin]

Back in the Sixties or maybe even the early seventies there was a song recorded by I believe a father and dauther duo that was played on the radio.
The Male would sing "Let's take a walk" the girl would sing dumity dum then the male "just a little walk" The girl again dumity dum then the male and so on. Let's take a walk hand in hand.
In a winter wonderland (I think). For some reason this tune keeps returning in my head yet I have no idea who sang it or whats it's title.

Any Ideas Many Thanks Jelte