When did this become a thing? Given that the weather has been unseasonably warm here in the midwest, I was wondering if anyone could shed some light on the matter.
The song "White Christmas", by Irving Berlin was first performed by Bing Crosby on the radio on Christmas Day 1941.
Crosby's version is thought to be the best selling single of all time.
The song then was included in the film "Holiday Inn" in 1942.
The whole "White Christmas" concept got a further boost in 1954, with the release of the film, "White Christmas" in which the song featured again.
Many other artists have also recorded the song.
I think the song "White Christmas", and its subsequent movie versions and covers, started and perpetuated this desire, so the answer to your question is: 1941.