I've had both the blue and green milk at Galaxy's Edge. It's actually not egg nog like, nor does it contain milk. It's vegan, and made from rice milk, coconut oil, and then fruit (flavoring?) of some sort. In the parks, you can get rum added to it. The blue is sweeter than the green, so I preferred the green. I enjoyed it a lot actually with the rum.
No, there's no milk in it. This is wrong. It's vegan and rice based.