What brands of milk do not have vitamin D3 added?

Try Rice Dream. Unfortunately, almost (if not all) cow milks contain D3.

Nondairy milks usually are fortified with D2, which is a plant source of Vitamin D.

Rice milk tastes nothing like soymilk, so it's definitely worth a try.
If there is a Giant market food store near you, I recommend buying Nature's Promise, since it is quite cheap and also has much more nutrition than Rice Dream.