With the holidays coming up this question seems relevant, so here it goes, would it be possible to make a vegan egg nog?
Traditional egg nog uses eggs, dairy, sugar, booze, and nutmeg. All of these are actually (lacto-ovo) vegetarian ingredients.
If you want to make a fully vegan "egg" nog, eggs and dairy can't be used. The good news, though, is that those aren't the primary flavor characteristics of the drink! I don't get nostalgic about drinking raw eggs, I'm interested in the nutmeg and sweetness -- and you can still include liquor, sugar, and nutmeg.
There are a lot of options available for replacing that "creamy" base of eggs and cream: non-dairy milks, tofu, cashew cream, and so on. (If your traditional egg nog is one that includes a foamy top layer, find a vegan whipped cream alternative.)