YouTube has these recordings:

Bing Crosby.

Marilyn Monroe, from the film "Some Like It Hot" (1959).

Nat King Cole.

p.s. I don't think the line "with icy, frigid air" was meant to be a reference to the Frigidaire brand of refrigerators, but I did hear one version where the line was changed to "like an icy Frigidaire." Now, was that deliberate, or a mondegreen?