Not all snakes have white bellies. Many species have patterned bellies (e.g. corn snakes, mud snakes, etc.) or brightly colored bellies (e.g. plain-bellied watersnake, ring-necked snake, redbelly snake). It varies by species.
I don't think there's a simple answer for why belly coloration varies in snakes. In ground-dwelling species such as some pythons and boas, belly color isn't necessary because it is never displayed. Pigments are actually energetically expensive to make, so if an animal doesn't have to make them, they generally don't and appear white. Snakes that use their bellies in displays to ward off predators, such as mud snakes, ringnecked snakes, etc., tend to have brightly colored bellies. Arboreal and semi-arboreal snakes tend to have patterned or at least pigmented bellies, probably to aid in camouflage if seen by a predator from below.
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