This crazy tune was written by the same person who wrote "I saw mommie kissing Santa Claus", the British songwriter Tommie Connor, he also wrote the the Gracie Fields' song "The Biggest Aspidistra in the World".
Alma Cogan had a number of fun hit records, my other favourite being (There's a railroad) In the middle of the house.
In Never do a tango with an Eskimo, the advice is mainly to a lady from Nebraska who may happen to be at a party in Alaska, so a slightly narrow field, but the advice may be sound, albeit anti Eskimo. The risks involved for the lady from Nebraska is that she will get a "breeze up" and may end up with a "freeze up". These don't necessarily sound like dangerous afflictions, but one never knows.
The song was also recorded in French by Petula Clark and marvellously retitled as Tango de L'Esquimau: Petula Clark at Myspace Music
Anyway here's a video someone made with penguins, followed by June Brown and Vincent Simone 'dancing' a tango on a Christmas edition of Strictly Come Dancing