Question about relation of Christmas to snow and winter.?

When Christmas comes, I seem to notice a very strong mental relation of the Christmas season to the Northern Hemisphere winter season. For instance, many christmas songs have winter related lyrics such as "snow," "frost," and "chill." Also, it seems that when people decorate for Christmas, especially in indoor areas like shopping malls, and in the deep southern states, a lot of people also put down white cotton to represent snow, plus they even spray that white stuff from spray cans on windows. I also even heard tales of people in, for instance southern Florida putting white cotton or spray stuff on their gr outside and even of people bringing "snow machines" to the Florida Keys for Christmas. Why exactly do people do that? And why exactly do people like to ociate the Christmas season so strongly with winter and snow? Especially since truthfully, only a comparatively small part of the Earth even gets snow at all during the Christmas season.