Why for Christmas?

I was listening to one of those all-Christmas, all-the-time radio stations this morning on my way in to work, and I had a thought about a couple songs I heard. What makes a song such as "My Favorite Things," "Let it Snow," or "Baby, it's Cold Outside," a Christmas song? There's no mention of the holiday in any of them, yet they're all played regularly during this time of year. There's no love of jingling bells, silent nights or reindeers put to music, and no fuzzy religious connotations: just raindrops and puppies, snow, and some guy trying to get some action from his prudish girlfriend. Is it just because someone, some mythical someone, decided that these songs sound Christmas-y? Couldn't they just be considered "winter" carols and featured anytime from the first snowfall to last snowfall, or just anytime, as for "Things"?
(And bonus points for those who will also make note that "My Favorite Things" is from The Sound of Music, a movie involving not only an almost-nun who turns away from the convent, but Nazis; an unnerving use of string puppets; horrificly green playclothes; and a German baroness who's just mean. Nothing at all in the spirit of the holiday.)

Now, the beauty of today's sock is that it features Olive, the Other Reindeer. For those who don't know the story, Olive is a dog, who didn't know she was a dog, and who figured that she must be a reindeer, based on the evidence of the line from the Rudolph song, "...all of the other reindeer...." (Trust me; if you sing it, it sounds right.) Anyway, in the story, Olive makes her way to the North Pole, meets Mr. Martini the penguin along the way, and saves Christmas from a nefarious postman. It's a totally cute story, and the little movie is adorable, so the socks were a must-buy when I saw them at the store.