My children only drink soymilk. When I was making my reservations, I asked the CM there and at dining about the availability of soy in the parks and resorts. They must have some type of search engine because she typed in soy milk and didn't get anything at all.
I am planning on having gardengrocer.com deliver groceries to us in our room. I guess they have soy milk (and I need some other soy speciality items too).
Sorry I couldn't answer your question!