In my experience, egg-nog is associated exclusively with Christmas and the holiday season. I suspect you would have a tough time even finding it in my local supermarket at other times of year. So how did egg-nog come to be associated with Christmas?
AFAICT, as the advent of cleaner water supplies made it less important for sanitary purposes to have some alcohol content in everything you drank, sweet confections like eggnog shifted from breakfast items to party drinks.
I’m going to guess that eggnog remained more of a winter party drink simply because rich creamy drinks are both more appealing and less likely to spoil in cold weather than in hot.
So at this point in time, it’s become a tautology. We only have egg-nog at Christmas, because they only make it at Christmas and they only make it at Christmas because we only buy it at Christmas.
The weather thing seems backwards in that egg-nog is usually served cold, but it’s also a heavy drink and calorie dense, which seems to go well with bracing yourself against cold weather.
Diabetic, I make it with splenda. Sugar is not a texturizer in this food, so it does not need to be a component [like it does in proper ice cream, unless you add lots of texturizers like carageenan and guar gums] the texture comes from the beaten whole eggs.
Probably the same people who buy other bottled drink mixes. My guess is that they’re either extremely lazy or fairly ignorant, because very few of these drinks really take much in the way of weird ingredients (save maybe the Mai-Tai (orgeat) and Hurricane(passion fruit juice/nectar)).